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B£>  9 


P*si)CHEMICAL    RESE/'   • ' 


1912-13 


UC-NRLF 


Sri  93 


THE  STAFF  OF  THE  BIOCHEMICAL 
LABORATORY 

THE  UNIVERSITY  OF  CHICAGO 

ALBERT  P.  MATHEWS 
Editor 


UNIVERSITY 


CHICAGO 
1914 


GIFT  OF 
Prof.   Jacques  Loeb 


BIOCHEMICAL   RESEARCH 

1912-13 


By 

THE  STAFF  OF  THE  BIOCHEMICAL 
LABORATORY 

THE  UNIVERSITY  OF  CHICAGO 

'I 

ALBERT  P.  MATHEWS 

Editor 


CHICAGO 
1914 


.V     «?. 


-  .<•••    :  .%  '  ">  BIOLOGY 

LHL/:A»  ujBftA.-.y 


BIOLOGf 

UBRARY 

G 

DEDICATED  TO  THE   MEMORY 
OF 

WALDEMAR  KOCH 

(April  8,  1875  —  February  i,  1911) 


CONTENTS 


1.  WALDEMAR  KOCH  By  Albert  P.  Mathews 

(Biochemical  Bulletin,  I,  372-76,  1912) 

2.  STUDIES  ON  THE  PHYSICAL  PROPERTIES  OF  PROTOPLASM 

By  G.  L.  Kite 

(American  Journal  of  Physiology,  XXXII,  146-64,  1913) 

3.  ON  THE  NATURE  OF  THE  IODINE  CONTAINING  COMPLEX 
IN  THYREOGLOBULIN  By  Fred  C.  Koch 

(Journal  of  Biological  Chemistry,  XIV,  101-16,  1913) 

4.  A  COMPARISON  OF  THE  BRAIN  OF  THE  ALBINO  RAT  AT  BIRTH 
WITH  THAT  OF  THE  FETAL  PIG  By  Mathilde  L.  Koch 

(Journal  of  Biological  Chemistry,  XIV,  267-79,  1913) 

5.  A  COMPARISON  OF  TWO  METHODS  OF  PRESERVING  NERVE 
TISSUE  FOR  SUBSEQUENT  CHEMICAL  EXAMINATION 

By  W.  Koch  and  M.  L.  Koch 

(Journal  of  Biological  Chemistry,  XIV,  281-82,  1913) 

6.  THE  CHEMICAL  DIFFERENTIATION  OF  THE  BRAIN  OF  THE 
ALBINO  RAT  DURING  GROWTH      By  W.  Koch  and  M.  L.  Koch 

(Journal  of  Biological  Chemistry,  XV,  423-46,  1913) 

7.  ADAPTATION  FROM  THE  POINT  OF  VIEW  OF  THE  PHYSIOLO- 
GIST By  A.  P.  Mathews 

(American  Naturalist,  XL VII,  90-103,  1913) 

8.  A   METHOD   OF   DETERMINING  "A"  OF  VAN  DER  WAALS'S 
EQUATION  By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  154-61,  1913) 

9.  THE  RELATION  OF  THE  VALUE  "A"  OF  VAN  DER  WAALS'S 
EQUATION  TO  THE  MOLECULAR  WEIGHT  AND  NUMBER  OF 
VALENCES  OF  THE  MOLECULE  By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  181-204,  1913) 

10.  THE  VALENCE  OF  CHLORINE  AS  DETERMINED  FROM  THE 
MOLECULAR  COHESION  OF  CHLORINE  COMPOUNDS 

By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  252-63,  1913) 
iii 


801295 


iv  CONTENTS 

11.  THE  VALENCE  OF  OXYGEN,  SULFUR,  NITROGEN  AND  PHOS- 
PHORUS DETERMINED  FROM  THE  MOLECULAR  COHESION 

By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  331-36,  1913) 

12.  THE   VALENCE   OF   THE   ARGON   GROUP   AS   DETERMINED 
FROM  THE  MOLECULAR  COHESION  By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  337~43,  1913) 

13.  A  NOTE  ON  THE  STRUCTURE  OF  ACETYLENE 

By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  320-21,  1913) 

14.  DO  MOLECULES  ATTRACT  COHESIVELY  INVERSELY  AS  THE 
SQUARE  OF  THE  DISTANCE?  By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  520-36,  1913) 

15.  THE    SIGNIFICANCE    OF    THE    RELATIONSHIP    BETWEEN 
MOLECULAR  COHESION  AND  THE  PRODUCT  OF  THE  MOLECU- 
LAR WEIGHT  AND  THE  NUMBER  OF  VALENCES 

By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  481-500,  1913) 

16.  THE  INTERNAL  PRESSURES  OF  LIQUIDS        By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVII,  603-28,  1913) 

17.  THE    QUANTITY    OF    RESIDUAL    VALENCE    POSSESSED    BY 
VARIOUS  MOLECULES  By  A.  P.  Mathews 

(Journal  of  Physical  Chemistry,  XVIII,  474,  1914) 

18.  AN   IMPORTANT   CHEMICAL   DIFFERENCE   BETWEEN   THE 
EGGS  OF  THE  SEA  URCHIN  AND  THOSE  OF  THE  STAR  FISH 

By  A.  P.  Mathews 
(Journal  of  Biological  Chemistry,  XIV,  465-67,  1913) 

19.  A  NEW  METHOD  AND  APPARATUS  FOR  THE  ESTIMATION  OF 
EXCEEDINGLY  MINUTE  AMOUNTS  OF  CARBON  DIOXIDE 

By  Shiro  Tashiro 

(American  Journal  of  Physiology,  XXXII,  136-44,  1913) 

20.  CARBON  DIOXIDE  PRODUCTION  FROM  NERVE  FIBRES  WHEN 
RESTING  AND  WHEN  STIMULATED;    A  CONTRIBUTION  TO 
THE  CHEMICAL  BASIS  OF  IRRITABILITY         By  Shiro  Tashiro 

(American  Journal  of  Physiology,  XXXII,  107-35,  1913) 


[Reprinted  from  THE  BIOCHEMICAL  BULLETIN,  1912,  i,  pp.  372-376.     March.] 


WALDEMAR  KOCH 


Herman  Koch,  a  mining  engineer  of  international  reputation, 
lived  in  Clausthal,  Hannover,  Germany.  His  father,  his  grand- 
father and  his  grandfather's  father  had  been  mining  engineers  be- 
fore him.  One  of  his  nine  sons  was  Robert  Koch,  the  great  bac- 
teriologist ;  another  was  Hugo  Koch,  also  a  mining  engineer ;  another, 
Arnold  Koch,  came  to  this  country  in  1867  with  letters  of  intro- 
duction from  Alfred  Nobel,  who  was  a  friend  of  Herman  Koch. 
Arnold  Koch  settled  in  St.  Louis,  where  his  only  son,  Waldemar* 
was  born  April  8,  1875. 

The  first  part  of  Dr.  Koch's  college  life  was  spent  in  Washington 
University,  St.  Louis,  but  his  last  year  he  spent  in  Harvard,  from, 
which  he  received  his  undergraduate  degree,  and  two  years  later,  in 
1900,  the  degree  of  Ph.D.  in  organic  chemistry.  He  was  then  for 
one  year,  assistant  in  physiology  in  the  Harvard  Medical  School  with 
Professor  Porter.  He  began  at  that  time  the  study  of  the  chem- 
istry of  the  nervous  system,  which  he  continued  until  his  death.  He 
came  to  the  University  of  Chicago  as  an  associate  in  physiological 
chemistry  in  1901,  and  with  a  short  interregnum  spent  in  teaching" 
pharmacology  and  physiological  chemistry  in  the  University  of  Mis- 
souri, he  remained  in  the  University  of  Chicago  continuously  there- 
after, where  at  the  time  of  his  death  he  was  associate  professor  of 
pharmacology.  He  was  for  a  time  with  Schmiedeberg  in  Strass- 
burg;  and  during  his  vacations  he  worked  for  several  years,  part 
of  the  time  under  a  grant  from  the  Rockefeller  Institute,  in  the  labo- 
ratory of  Dr.  Mott  in  the  Claybury  Asylum  for  the  Insane,  near 
London;  afterwards  for  one  season  he  was  on  the  staff  of  the  new 
hospital  for  the  insane  at  Long  Grove,  near  London;  and  for  the 
past  year  he  had  been  connected,  also,  with  the  Wistar  Institute  of 
Anatomy  in  Philadelphia.  In  these  various  institutions  he  had  un- 
usual opportunities,  which  he  utilized  to  the  utmost,  for  the  study 
of  pathological  and  normal  nervous  material. 

Dr.  Koch's  work  on  the  chemistry  of  the  nervous  system  is 

372 


373 


Waldemar  Koch  [Mar. 

£>  a;ll  physiological  chemists.  The  chemistry  of  the  brain 
is  'a  very  'difficult  field  and  the  separation  of  the  lipoid  substances 
is  stifl  hardly  possible.  He  spent  the  greater  part  of  these  years  in 
devising  accurate  methods  of  quantitative  analysis.  These  methods 
had  been  so  perfected  that  he  had  secured  more  complete  and  more 
accurate  quantitative  analyses  of  nervous  tissue  than  any  hitherto 
made.  By  means  of  these  methods  he  was  attacking  the  problem 
of  the  differentiation  of  the  brain  during  growth;  the  distribution 
of  various  substances  in  different  parts  of  the  brain;  variations  in 
composition  during  disease;  and  the  differences  between  the  brains 
of  different  animals.  He  was  also  engaged  in  separating  carefully 
the  various  lipoids,  such  as  kephalin  and  lecithin,  and  in  examining 
their  composition.  He  showed  the  very  important  fact  that  kepha- 
lin exists  as  a  potassium  salt,  whereas  lecithin  has  more  of  an 
affinity  for  sodium.  His  method  of  purification  of  the  lipoids  by 
precipitation  with  chloroform  and  hydrochloric  acid  was  extremely 
useful.  Among  his  other  important  contributions  must  be  men- 
tioned his  work  on  the  behavior  of  lecithin  and  kephalin  emulsions 
towards  various  salts,  anesthetics  and  drugs,  work  which  showed 
one  way  in  which  these  substances  might  influence  irritability.  He 
discovered,  also,  that  the  brains  of  persons  having  the  very  obscure 
insanity,  dementia  praecox,  contained  less  of  a  certain  sulfur  frac- 
tion than  usual,  and  in  his  further  examination  of  the  sulfur  dis- 
tribution in  the  brain  he  isolated  a  lipoid-sulfur  compound  of  very 
interesting  nature.  He  had  prepared  a  considerable  quantity  of 
this  compound  and  he  was  engaged  in  studying  its  nature  at  the 
time  of  his  death. 

Dr.  Koch's  interest  from  the  first  had  been  in  the  problem  of 
the  action  of  drugs  on  the  nervous  system.  He  taught  pharma- 
cology almost  from  the  time  of  his  graduation.  He  fitted  himself 
for  his  duties  as  a  teacher  by  taking  the  regular  medical  courses  in 
pathology,  anatomy,  embryology  and  many  of  the  clinical  courses, 
as  well  as  by  studying  with  Schmiedeberg  in  Germany.  He  thus 
had  a  very  unusually  broad  training  and  was  able  to  look  at  his 
subject  from  all  sides,  the  chemical,  the  biological,  and  the  clinical. 
There  are  very  few  men  in  pharmacology  to-day,  who  possess  his 
extensive  knowledge  and  his  sane,  scientific  and  broad  point  of  view. 


i9i2]  Albert  P.  Mat  hews  374 

The  work  he  was  doing  on  the  nervous  system  he  regarded  as 
fundamental  work  in  pharmacology,  necessary  before  any  real  sci- 
ence of  pharmacology  could  be  constructed.  He  had  just  reached 
a  point  when  the  direct  application  of  his  methods  to  the  solution  of 
the  problem  of  how  drugs  combine  with  nerve  cells  could  be  begun. 
To  die  at  such  a  time  was  particularly  cruel.  Had  he  lived  a  few 
years  longer  his  recognition  as  one  of  the  leading  pharmacologists 
of  the  world  would  undoubtedly  have  been  assured.  His  work,  like 
that  of  his  uncle,  Robert  Koch,  was  very  thorough  and  exact,  and 
he  proceeded  in  logical  order  to  overcome  one  difficulty  after  another. 

Dr.  Koch's  personality  won  him  many  friends.  He  was  a  true, 
loyal  and  courageous  friend,  entirely  honest  and  of  sane  judgment; 
he  avoided  making  enemies,  as  far  as  possible.  He  was  fond  of 
out  of  doors,  and  loved  the  hills,  rivers  and  fields,  and  tramping  in 
the  dunes  near  Chicago  was  his  main  recreation.  He  had  a  keen 
appreciation  of  what  was  fine  in  music  and  in  art.  His  was  an 
open,  frank,  kindly  nature,  considerate  of  others  and  slow  to  anger. 

His  death  by  pneumonia,  February  ist,  at  the  early  age  of 
thirty-six,  was  an  irreparable  loss  to  his  friends,  to  his  University 
and  to  science. 

PAPERS  PUBLISHED  BY  DR.  WALDEMAR  KOCH 

KOCH  (and  C.  LORING  JACKSON).  Die  Einwirkung  des  Jods  auf  das 
Bleisalz  des  Brenzcatechins.  Berichte  der  deutschen  chemischen 
Gesellschaft,  1898,  xxxi,  1457. 

(and  C.  LORING  JACKSON).    On  the  action  of  sodic  ethylate  on 

tribromdinitrobenzol.     Proceedings  of  the  American  Academy  of 
Arts  and  Sciences,  1898,  xxxiv,  119. 

(and  C.  LORING  JACKSON).     On  certain  derivatives  of  ortho- 

benzoquinone.    Ibid.,  1900,  xxxvi,  1*97. 

The  physiological  action  of  formaldehyde.    American  Journal  of 

Physiology,  1902,  vi,  325. 

Zur  Kenntniss  des  Lecithins,  Kephalins,  und  Cerebrins  aus  Ner- 

vensubstanz.       Zeitschrift     fiir     physiologische     Chemie,     1902, 
xxxvi,  134. 

The  lecithans.    Their  function  in  the  life  of  the  cell.    Decennial 

Publications,  Chicago  (University  of  Chicago  Press),  1902,  x,  93. 

Some  corrosions   found  on  ancient  bronzes.     Science    (n.   s.), 

1903,  xvii,  152. 


375  Waldemar  Koch  [Mar. 

Die  Lecithane  und  ihre  Bedeutung  fiir  die  lebende  Zelle.     Zeit- 

schrift  fiir  physiologische  Chemie,  1903,  xxxvii,  181. 

Methods  for  the  quantitative  chemical  analysis  of  the  brain  and 

cord.    American  Journal  of  Physiology,  1904,  xi,  303. 

—  On  the  origin  of  creatinin.    Ibid.,  1905,  xiii,  19. 

—  On  psychic  secretion.    Ibid.,  1905,  xiii,  37. 

-  Relation   of   creatinin   excretion   to   variations   in    diet.      Ibid., 
1905,  xv,  15. 

On  the  presence  of  a  sulphur  compound  in  nerve  tissue.    Science 

(n.  s.),  1905,  xxi,  884. 

Lecithin   in   infant   feeding.      St.   Louis   Courier   of   Medicine, 

1905,  xxvi,  June. 

A   study   of   the   metabolism    of    the    nervous    system.      Ibid., 

1906,  xv ;   Proceedings   of  the   American   Physiological    Society 
p.  xv  (December,  1905). 

(and  W.  H.  GOODSON).     A  preliminary  study  of  the  chemistry 

of  nerve  tissue  degeneration.    Ibid.,  1906,  xv,  272. 

-  (and  HERBERT  S.  WOODS).     The  quantitative  estimation  of  the 
lecithans.    Journal  of  Biological  Chemistry,  1906,  i,  203. 

tiber   den   Lecithingehalt   der   Milch.      Zeitschrift    fiir   physio- 
logische Chemie,  1906,  xlvii,  327. 

(and  HOWARD  S.  REED).    The  relation  of  extractive  to  protein 

phosphorus  in  Aspergillus  niger.    Ibid.,  1907,  iii,  49. 

The   relation   of   electrolytes   to   lecithin   and   kephalin.      Ibid., 

1907,  iii,  53. 

The   quantitative   estimation   of    extractive   and    protein   phos- 
phorus.   Ibid.,  1907,  iii,  159. 

Some  chemical  observations  on  the  nervous  system  in  certain 

forms  of  insanity.    Archives  of  Neurology,  1907,  iii,  331. 

Zur  Kenntniss   der  Schwefelverbindungen   des   Nervensystems. 

Ibid.,  1907,  liii,  496. 

—  (and  S.  A.  MANN).    A  comparison  of  the  chemical  composition 
of  three  human  brains  at  different  ages.     Journal  of  Physiology 
(English),  1907,  xxxvi;  Proceedings  of  the  Physiological  Society, 
p.  xxxvi  (Nov.  23). 

-  Phosphorus  compounds  as  brain  foods.     Journal  of  the  Amer- 
ican Medical  Association,  1909,  Hi,  1381. 

-  (and  S.  A.  MANN).    A  chemical  study  of  the  brain  in  healthy 
and    diseased    conditions,    with    special    reference    to    Dementia 
praecox.    Archives  of  Neurology  and  Psychiatry,  1909,  iv,  31. 


•  Albert  P.  Mathews  376 

•  Methods  for  the  quantitative  chemical  analysis  of  animal  tissues. 

i.  General  principles.    Journal  of  the  American  Chemical  Society, 
1909,  xxxi,  1329. 

(and  S.  A.  MANN).    2.  Collection  and  preservation  of  material. 

Ibid.,  1335. 

(and  EMMA  P.  CARR).     3.  Estimation  of  the  proximate  constit- 
uents.    Ibid.,  1341. 

(and  F.  W.  UPSON).    4.  Estimation  of  the  elements,  with  special 

reference  to  sulphur.     Ibid.,  1355. 

— —  Die   Bedeutung  der   Phosphatide    (Lecithane)    fiir  die  lebende 
Zelle.    II.    Zeitschrift  fiir  physiologische  Chemie,  1909,  Ixiii,  432. 

(and  F.  W.  UPSON).    The  distribution  of  sulphur  compounds  in 

brain  tissue.     Proceedings  of  the  Society  for  Experimental  Biol- 
ogy and  Medicine,  1909,  vii,  5. 

Phosphorus  compounds  as  brain  foods.     Journal  of  the  Amer- 
ican Medical  Association,  1909,  Hi,  1381. 

Zur  Kenntniss  der  Schwefelverbindungen  des   Nervensystems. 

II.      tiber    ein    Sulfatid   aus    Nervensubstanz.      Zeitschrift    fiir 
physiologische  Chemie,  1910,  Ixx,  94. 

Pharmacological  studies  on  the  phosphatids.     i.  Methods  for  the 

study  of   their  combinations  with  drugs   and  other   substances. 
Journal  of  Pharmacology  and  Experimental  Therapeutics,  1910, 
«,  239. 

(and  F.  H.  PIKE).     2.  The  relation  of  the  phosphatids  to  the 

sodium  and  potassium  of  the  neuron.     Ibid.,  245. 

(and  F.  C.  MCLEAN).     3.  The  relation  of  the  phosphatids  to 

Overton  and  Meyer's  theory  of  narcosis.     Ibid.,  249. 

—  (and  A.  W.  WILLIAMS).    4.  The  relation  of  brain  phosphatids 
to  tissue  metabolites.     Ibid.,  253. 

—  (and  H.  T.  MOSTROM).    5.  The  function  of  the  brain  phospha- 
tids in  the  physiological  action  of  strychnin.     Ibid.,  265. 

—  Recent  studies  on  lipoids.     Journal  of  the  American  Medical  As- 
sociation, 1911,  Ivi,  799. 

ALBERT  P.  MATHEWS. 

University  of  Chicago. 


STUDIES    ON    THE    PHYSICAL    PROPERTIES    OF 
PROTOPLASM 


Reprinted  from  the  American  Journal  of  Physiology 
Vol.  XXXII -June  2,  1913 -No.  II 


STUDIES   ON  THE  PHYSICAL  PROPERTIES   OF 
PROTOPLASM 

I.    THE  PHYSICAL  PROPERTIES  OF  THE  PROTOPLASM  OF  CERTAIN 
ANIMAL  AND  PLANT  CELLS 

BY  G.  L.  KITE 

[From  the  Hull  Laboratories  of  Biochemistry  and  Pharmacology,  University  of  Chicago] 

INTRODUCTION 

\  LTHOUGH  the  living  substance  of  animal  and  plant  cells 
-^A-  was  correctly  interpreted  by  Dujardin  and  von  Mohl  in 
the  second  quarter  of  the  nineteenth  century,  almost  nothing  is 
definitely  known  of  the  physical  state  of  protoplasm.  Properties 
described  by  such  adjectives  as  glutinous,  slimy  and  hyaline  were 
recognized  by  the  early  micro^copists,  who  were  forced  to  study  liv- 
ing cells  and  tissues. 

During  the  last  fifty  years  an  extensive  literature  has  grown  up  on 
the  subject  of  the  structure  of  protoplasm.  For  the  purposes  of 
this  paper,  these  investigations  may  be  divided  into  two  groups.  The 
first  group  comprises  those  studies  on  the  structure  of  protoplasm, 
made  with  the  aid  of  fixatives.  A  large  part  of  our  knowledge  of 
the  morphology  of  the  cells  and  tissues  of  animals  and  plants  is  the 
direct  result  of  the  development  of  fixing  methods. 

The  errors  involved  in  the  attempts  to  determine  the  true  molar 
structure  of  protoplasm  by  the  use  of  fixing  reagents  have  been  pointed 
out  particularly  by  Flemming,1  Berthold,2  Schwarz,3  Fischer,4  and 
Hardy.5  In  this  connection,  it  will  suffice  to  state  that  Hardy's  con- 
clusion that  fixing  reagents  always  cause  structural  changes  in  pro- 

1  FLEMMING:  Zellsubstanz,  Kern  und  Zelltheilung,  1882,  Leipzig. 

2  BERTHOLD:   Studien  iiber  Protoplasmamechanik,  1886,  Leipzig. 

3  SCHWARZ:  Cohn's  Beitrage  zur  Biologic  der  Pflanzen,  1887,  v,  p.  i. 

4  FISCHER:  Archiv  fur  Entwicklungsmechanik,  1901,  xiii,  p.  i. 

5  HARDY:  Journal  of  physiology,  1899,  xxiv,  p.  158. 


Physical  Properties  of  Protoplasm  147 

toplasm  that  are  frequently  very  different  from  the  normal  living 
substance,  has  never  been  refuted.  Hence,  at  least,  it  does  not  seem 
that  more  than  an  approximation  of  the  actual  structure  of  pro- 
toplasm can  be  attained  by  the  use  of  fixatives.  Besides,  this  method 
is  worthless  as  a  means  of  investigating  the  physics  of  protoplasm. 

The  papers  that  fall  in  the  second  group  deal  with  the  study  of 
living  cells.  Strassburger,6  Wilson,7  Foot  and  Strobell,8  Lundegardh9 
and  others  have  shown  that  many  of  the  structural  elements  of  the 
mi  to  tic  figure  can  be  seen  in  living  animal  and  plant  cells.  Numerous 
investigators  have  pointed  out  the  presence  of  granules,  vacuoles, 
and  fibrils  in  various  types  of  unfixed  cells;  but  for  the  most  part, 
the  studies  on  living  cells  have  been  made  for  the  purpose  of  decreas- 
ing the  error  due  to  the  use  of  fixing  reagents. 

All  such  investigations  are  open  to  several  sources  of  error. 
Hardy 10  writes  that  the  process  of  dying  produces  structural  changes 
in  the  cell  substance,  since  coagulation  appears  to  occur  in  all  dying 
cells.  Many  cells  are  certainly  quickly  asphyxiated  when  mounted 
for  microscopical  examination  in  the  usual  manner.  I  have  been 
able  to  overcome,  largely,  this  source  of  error,  by  the  use  of  an  open- 
end  moist  chamber,  that  does  not  appear  to  interfere  with  normal 
respiration. 

A  second  source  of  error  is  due  to  the  nature  of  the  optical  prin- 
ciples involved  in  microscopical  vision.  Many  years  since  Abbe  u 
demonstrated  that  the  optical  image  is  a  diffraction  pattern  produced 
by  the  object  and  that  under  certain  conditions  the  image  may  be 
quite  different  from  the  object.  More  recently,  Porter,12  experi- 
menting under  ordinary  working  conditions,  has  described  a  number 
of  interesting  examples  of  this  sort.  Porter12  says,  "Images  were 
formed  which  were  utterly  false  in  their  smaller  details,  and  other 
images  were  profoundly  modified  by  the  presence  of  structure  lying 

6  STRASBURGER:  Zellbildung  und  Zelltheilung,  Jena,  1880,  iii.    Auflage. 

7  WILSON:  Journal  of  morphology,  1899,  xv,  Suppl. 

8  FOOT  and  STROBELL:  American  journal  of  anatomy,  iv,  p.  199. 

9  LUNDEGARDH:  Jahrbiicher  fur  wissenschaftliche  Botanik,  li,  p.  236. 

10  HARDY:  Journal  of  physiology,  1899,  xxiv,  p.  158. 

11  ABBE:   Archiv  fur  mikroskopische  Anatomic,   1874,  ix,  p.  413;    Gesam- 
melte  Abhandlungen,  1904,  i,  p.  45. 

12  PORTER:  Philosophical  magazine,  1906,  xi,  p.  154. 


i48  G.  L.  Kite 

entirely  beyond  the  focal  plane."  Such  facts  should  serve  to  make 
it  evident  that  one  can  easily  fall  into  error  in  interpreting  the  optical 
image  of  a  living  cell.  Porter12  recommends  "  a  working  knowledge 
of  the  phenomena  and  laws  of  diffraction,"  as  a  safeguard  against 
this  form  of  error. 

The  third  and  by  far  the  most  important  source  of  error  is  due 
to  the  peculiar  and  little  known  optical  properties  of  living  matter. 
The  phenomena  of  reflection,  refraction,  absorption,  dispersion,  inter- 
ference, diffraction  13  and  a  scattering  action  on  light 14  are  all  exhib- 
ited by  this  substance,  with  the  result  that  a  correct  interpretation 
of  the  image  of  a  living  cell  is  frequently  impossible.  Further- 
more, many  cells  are  so  opaque  and  turbid  that  the  interior  is  not 
visible.  Cloudiness  or  turbidity  is  almost  a  universal  property  of 
protoplasm  and  appears  to  be  due  chiefly  to  dispersion,  refraction, 
diffraction,  and  the  scattering  action  on  light  of  the  colloidal  par- 
ticles which  may  be  considered  as  the  real  structural  units  of  all 
protoplasm. 

Globules,  granules  and  cell  walls  frequently  show  diffraction 
halos  that  are  difficult  to  interpret  in  undissected  cells. 

The  aim  of  this  investigation  is  to  determine  the  physical  state 
and  the  molar  structure  of  protoplasm.  The  methods  are  radically 
different  from  those  heretofore  used,  and  are  believed  to  be  adequate 
for  this  purpose.  Dissection  and  vital  staining  are  used  to  deter- 
mine the  truthfulness  of  the  optical  image  and  the  actual  structure 
of  cells.  Unfortunately,  the  amount  of  the  error  involved  in  the 
employment  of  these  methods  depends  entirely  on  the  skill  of  the 
experimenter;  but  it  is  believed  that  the  error  becomes  quite  small 
with  complete  mastery  of  the  methods. 

The  structural  changes  that  cells  may  undergo  during  the  time 

13  Excellent  expositions  of  the  principles  of  physical  optics  are  given  by: 
WOOD,  R.  W:    1911,  Physical  Optics;   DRUDE,  P.:    1912,  Lehrbuch  der  Optik; 
PRESTON:  1901,  Theory  of  Light. 

14  Lord  Rayleigh  (Philosophical  magazine,  xli,  p.  107)  has  pointed  out  that 
reflection  and  refraction  have  no  application  unless  the  surface  of  the  disturbing 
body  is  larger  than  many  square  wave-lengths.     The  turbidity  of  protoplasmic 
sols,  then,  is  due  entirely  to  the  scattering  action  on  light  of  the  minute  aggre- 
gates of  the  disperse  phase,  while  reflection,  refraction,  diffraction,  dispersion 
and  a  scattering  action  on  light  are  all  seemingly  involved  in  the  production  of 
turbidity  by  gels. 


Physical  Properties  of  Protoplasm  .          149 

required  for  their  dissection  is  a  possible  source  of  error  that  may 
appear,  at  first  sight,  to  be  very  difficult  to  control.  Certainly 
many  biologists  hold  the  view  that  cells  rapidly  undergo  important 
morphological  changes  following  mechanical  injury.  With  few 
exceptions  it  has  not  been  found  difficult  to  follow  the  structural 
changes  that  occur  in  cells  that  are  being  dissected;  but  the  really 
remarkable  fact  is  the  marked  slowness  of  such  death  changes 
as  granulation,  fragmentation  and  general  coagulation,  following 
mechanical  injury. 

It  seems  best  to  limit  this  introductory  paper  to  a  description  of 
selected  types  of  widely  different  cells  and  in  future  publications  to 
treat  systematically,  selected  types  of  the  principal  phyla  of  animals 
and  the  chief  groups  of  plants. 

The  special  literature  bearing -on  this  investigation  will  be  dis- 
cussed in  subsequent  papers.  , 

A  review  of  such  well-known  theories  as  those  of  Butschli, 
Flemming  and  Altmann  lies  outside  the  province  of  this  paper. 

METHODS  AND  MATERIAL 

The  development  of  a  really  adequate  method  for  the  dissection 
of  living  cells,  under  the  highest  powers  of  the  microscope,  has  made 
possible  this  study.  The  principles  of  this  method  are  simple.  The 
dissecting  instrument  is  a  glass  needle  that  may  measure  less  than 
one  micron  in  diameter  and  is  drawn  on  the  end  of  a  piece  of  special 
Jena  glass  tubing  about  200  mm.  long  and  4  mm.  in  diameter.  The 
needle  is  held  in  a  three-movement  Barber  pipette  holder.  The  cell 
chosen  for  dissection  is  mounted  in  a  hanging  drop  in  an  open-end 
moist  chamber  and  held  in  place  by  water-glass  surface  tension, 
which  can  be  varied  at  will. 

Both  diffuse  sunlight  and  artificial  light  are  used  as  sources  of 
illumination.  For  the  latter  a  Nernst  Glower  has  been  found  satis- 
factory, but  all  the  light  waves  outside  of  450  and  670  p>p*  are  cut  out 
by  the  use  of  appropriate  ray  screens.  The  same  means  is  used  to 
remove  enough  of  the  orange  and  red  rays  to  make  the  transmitted 
light  perfectly  white.  Such  light  is  composed  of  the  waves  that  are 
least  injurious  to  living  cells.  A  special  condenser  15  of  a  focal  dis- 
15  The  condenser  was  made  by  E.  Leitz  &  Co.,  Wetzlar. 


G.  L.  Kite 

stance  of  about  20  mm.,  a  2  mm.  apochromatic  objective,  compensat- 
ing oculars,  and  a  number  of  vital  stains,  are  necessary  additions. 

An  open-end  moist  chamber  25x60x15  mm.  has  been  found 
satisfactory.  The  bottom  is  separated  into  three  compartments  by 
very  small  glass  rods  and  water  is  placed  in  the  end  compartments. 
If  water  be  put  in  the  middle  compartment  it  may  decrease  the 
efficiency  of  the  condenser.  The  chamber  is  held  in  a  mechanical 
stage  and  most  of  the  dissections  are  made  by  quick  movements  of 
the  chamber  and  therefore  of  the  cell  being  dissected,  the  needle 
remaining  fixed. 

The  use  of  acetylene  which  can  be  burned  in  a  glass  micro-burner 
has  greatly  simplified  the  making  of  extremely  fine  needles.  An 
acetylene  flame  that  is  so  small  that  it  is  invisible  in  a  well-lighted 
room  can  be  kept  alive. 

The  more  important  of. the  vital  stains  used  include  methylene 
blue,  new  methylene  blue  N  (Cassella  Color  Co.),  new  methylene 
blue  GG  (Cassella  Color  Co.),  new  methylene  blue  R  (Cassella  Color 
Co.),  janus  green  (Metz  &  Co.),  pyronin  (Griibler),  vusuvin  (Griibler), 
toluidin  blue  (Griibler),  neutral  red  (Griibler). 

The  chief  structural  components  of  a  cell  can  usually  be  quickly 
brought  out  by  using  a  large  enough  number  of  vital  stains,  thus 
effecting  a  great  economy  of  time,  when  the  dissection  of  the  unstained 
cell  is  made. 

Barber's 16  isolation  and  intracellular  injection  methods,  vari- 
ously modified,  are  frequently  employed  to  supplement  and  control 
the  data  obtained  by  dissection. 

Nomenclature  Employed.  —  The  current  nomenclature  of  de- 
scriptive physics,  physical  optics  and  colloidal  chemistry  will  be 
employed.  Such  physical  properties  as  solidity,  tenacity,  elasticity, 
hardness  and  viscosity  have  been  determined  for  the  cells,  so  far 
studied.  In  general,  the  term  viscosity  will  be  used  to  designate  the 
degree  of  rigidity  of  protoplasmic  structures,  but  such  a  structure  as 
a  vitelline  membrane  may  be  comparatively  soft  and  yet  have  what 
must  be  considered  as  a  high  internal  friction  or  viscosity.  Elasticity 
is  determined  by  transfixing  a  selected  piece  of  a  cell  and  stretching 
it  and  observing  the  power  of  resumption  of  the  original  form.  Dis- 

16  BARBER:  University  of  Kansas  Science  Bulletin,  1907,  iv,  p.  3;.  Journal 
of  infectious  diseases,  1911,  viii,  p.  248;  ibid.,  1911,  ix,  p.  117. 


Physical  Properties  of  Protoplasm  151 

section  is  the  method  employed  for  determining  such  properties  as 
solidity,  hardness  and  tenacity  or  cohesiveness.  All  physical  proper- 
ties that  have  been  enumerated  are  relative  and  it  is  hoped  at  a  later 
time  to  increase  the  accuracy  of  description  by  the  selection  of  arbi- 
trary standards.  The  usage  of  the  terms  employed  in  this  paper  is 
based  on  the  dissection  of  many  widely  different  types  of  animal 
and  plant  cells. 

Living  matter  occupies  an  intermediate  position  between  true 
solids  and  true  liquids  and  has  many  of  the  properties  of  both  as 
well  as  properties  peculiar  to  itself.  It  belongs  to  the  class  of  colloids 
known  as  emulsoids  and  exists  in  either  a  gel  (hydrogel)  or  a  sol 
(hydrosol)  state.17  The  term  gel  will  be  used  to  designate  the  amor- 
phous semi-solid  state  and  sol  the  apparently  homogeneous  liquid 
state,  of  living  substance.  Protoplasmic  sols  usually  appear  as  hazy 
homogeneous  liquids  on  account  of  the  very  minute  size  of  the  protein 
aggregates  that  compose  the  solid  phase.  On  the  other  hand  pro- 
toplasmic gels  are  characterized  by  the  large  size  of  the  particles  of 
the  solid  phase  which  set  to  form  the  gel.  Hence,  living  gels  may 
exhibit  either  a  homogeneous  or  heterogeneous  molar  structure. 

It  should  now  be  clear  that  the  term  homogeneous  is  used  in  a 
relative  sense  to  describe  the  optical  image  and  refers  only  to  the 
molar  structure  that  can  be  brought  out  by  the  usual  microscopical 
powers  and  further  that  heterogeneity  is  the  universal  distinguishing 
characteristic  of  colloidal  sols  and  gels.  In  this  connection  it  may  be 
noted  that  Pauli18  states  that  the  " unfixed"  gel  of  gelatine  is  not 
structured  in  the  sense  of  being  composed  of  threads,  networks, 
granules  and  vacuoles;  it  has  the  molar  structure  of  a  one-phase  sys- 
tem,'which  is  precisely  what  is  meant  by  the  term  homogeneous  as 
used  in  this  paper;  the  molecular  structure  is  unknown.  The 
present  unsettled  state  of  the  problem  of  phase  relations  of  colloidal 

17  For  discussion  of  the  classification  of  colloids  see:  No  YES,  A:  1905,  Journal 
of  the  American  Chemical  Society,  1905,  xxvii,  p.  85;    OSTWALD,  Wo.:    1907, 
Zeitschrift  fur  Chemie  und  Industrie  der  Kolloide,   1907,  i,  p.   291;    PERRIN, 
J.:  1905,  Journal  de  la  chemie  physique,  iii,  p.  50;    FREUNDLICH  and  NEU- 
MANN, 1908,  Kolloid  Zeitschrift  iii,  p.  80;  VON  WEIMARN,  P.  P.:  ibid.,  1908,  iii, 
p.  26. 

18  PAULI:   Der  Kolloidale  Zustand  und  die  Vorgange  in  der  lebendigen  Sub- 
stanz,  Braunschweig,  1902. 


152  G.  L.  Kite 

solutions  has  been  ably  discussed  in  a  recent  paper  by  Hardy.19  It 
is  usual  to  regard  colloidal  systems  as  consisting  of  two  phases,  a  solid 
and  a  liquid,  which  have  been  termed  by  Wo.  Ostwald  20  the  dis- 
perse phase  and  the  dispersion  medium,  respectively. 

For  convenience  of  description  arbitrary  meanings  will  be  given 
the  terms  microsome  and  globule;  the  former  will  be  restricted  to 
minute  dense  masses  of  gel,  the  latter  to  suspensions  in  protoplasm 
that  show  many  of  the  physical  properties  of  oil  droplets  and  besides 
are  usually  free  of  protoplasm  when  dissected  out  of  a  cell.  Most  of 
the  suspensions  so  far  found  in  cells  fall  into  one  or  the  other  of 
these  groups,  but  intermediate  forms  have  been  observed. 


THE  EGG  or  ASTERIAS 

The  egg  of  Asterias  is  surrounded  by  a  mass  of  either  transparent 
or  translucent  jelly  which  is  soft  and  somewhat  elastic  and  glutin- 
ous; but  it  can  be  cut  and  torn  to  pieces  and  removed  from  the  egg 
with  little  difficulty.  Thirty-four  and  six-tenths  microns  is  the 
average  thickness  of  this  jelly.  This  structure  has  a  low  viscosity 
for  a  gel  and  is  therefore  extremely  dilute.  On  many  eggs,  the  jelly 
has  become  turbid  and  undergone  a  change  in  refractive  power  and 
as  a  result  is  visible  in  the  usual  microscopical  examination.  The 
inner  surface  of  the  jelly  envelope  is  closely  applied  to  the  outer 
surface  of  the  vitelline  membrane  which  is  invisible  except  in  eggs 
that  have  maturated.  The  vitelline  membrane  of  the  immature 
starfish  egg  is  a  transparent  and  invisible  solid  of  about  two  microns 
in  thickness.  The  physical  properties  of  this  structure  are  •  very 
definite  since  it  exhibits  extraordinarily  high  viscosity,  elasticity  and 
tenacity.  A  small  piece  can  be  drawn  out  into  a  mere  thread  and 
when  freed  the  thread  contracts  to  a  more  or  less  rounded  mass. 
During  maturation  the  vitelline  membrane  swells  to  two  and  three 
times  its  original  thickness,  undergoes  a  change  in  refractive  index, 
and  becomes  quite  cloudy  and  hence  visible.  In  this  state  it  is 
softer,  more  glutinous  and  less  rigid.  The  inner  surface  of  this 

19  HARDY:  Proceedings  of  the  Royal  Society,  Series  A,  1912,  Ixxxvi,  p.  601. 

20  OSTWALD:    Zeitschrift  fur  chemie  und  Industrie   der   Kolloide,    1907,  i, 
p.  291. 


Physical  Properties  of  Protoplasm  153 

membrane  is  tightly  glued  to  the  surface  of  the  cytoplasm,  from 
which  it  can  be  dissected  only  with  considerable  difficulty. 

The  misleading  optical  phenomena  that  are  involved  in  a  study  of 
the  cytoplasm  are  of  great  interest. 

It  is  usual  for  cytologists  to  consider  the  echinoderm  egg  a  classi- 
cal example  of  the  alveolar  structure  of  protoplasm.  No  one  can 
question  the  fact  that  beautiful  round  spaces  with  hazy,  protoplasmic 
walls  in  which  are  embedded  minute  granules,  can  be  seen  in  such 
eggs.  Biitschli  supposed  these  spaces  to  be  filled  with  a  watery  fluid. 

What  is  the  true  structure  of  the  cytoplasm  of  the  egg  of  Asterias? 
Careful  dissections  give  a  clear-cut  answer  to  this  question. 

The  cytoplasm  is  a  quiet  translucent  gel  of  comparatively  high 
viscosity;  it  can  be  drawn  out  into  large  strands,  but  is  not  cohesive 
and  elastic  enough  to  form  small  threads.  It  can  be  cut  into  small 
pieces  with  comparative  ease.  Fragments  usually  become  spherical, 
though  in  some  cases  water  is  slowly  taken  up  and  the  mass  changes 
into  the  sol  state.  Minute  granules  measuring  little  more  than  one 
micron  are  scattered  plentifully  throughout  the  cytoplasmic  gel. 
It  has  been  found  impossible  to  free  these  structures  completely  from 
the  gel  in  which  they  are  embedded.  They  are  optically  more  dense 
and  have  a  different  refractive  index  from  the  surrounding  living 
substance.  A  part  of  the  total  mass  of  cytoplasm  is  composed  of 
what  appears  to  be  alveoli  or  spaces;  but  a  careful  dissection  of  such 
an  alveolus  reveals  the  presence  of  a  globule  that  has  many  of  the 
optical  properties  of  an  oil  drop.  Such  a  globule,  freed  from  cyto- 
plasm, does  not  dissolve  in  sea  water  and  in  a  light  of  low  intensity 
exhibits  the  usual  diffraction  halo.  The  invisibility  of  liquid  drop- 
lets of  rather  high  viscosity  when  embedded  in  the  cytoplasm  might 
at  first  sight  appear  difficult  to  explain.  This  invisibility  is  due  to 
the  fact  that  the  refractive  index  and  dispersive  power  of  the  globules 
is  very  near  that  of  sea  water;  also,  the  optical  density  of  the  cyto- 
plasm is  evidently  higher  than  that  of  the  globule.  No  diffraction 
rings  could  be  seen  surrounding  the  globules  when  they  were  imbedded 
in  cytoplasm.  Centrifugal  force  dislodges  the  globules,  proving  them 
to  be  merely  suspended  in  a  living  gel.  The  minute  granules  respond 
much  less  readily  to  centrifugal  force.  Besides  they  show  optical 
properties  —  their  index  of  refraction  is  certainly  higher  than  that  of 
the  surrounding  gel  —  that  ally  them  to  highly  concentrated  particles 


154 


G.  L.  Kite 


of  the  cytoplasmic  gel.  Yet  it  seems  likely  that  all  such  structures 
as  granules  and  globules  must  be  considered  as  having  separated 
out  of  the  disperse  phase  and  to  be  therefore  of  the  nature  of 
suspensions.  The  living  cytoplasm,  then,  is  an  apparently  homo- 
geneous and  very  viscous  gel  in  which  microsomes  and  globules  are 
suspended. 

If  the  nucleus  of  the  immature  starfish  egg  be  dissected  out  in  sea 
water  it  undergoes  no  appreciable  change.  Dissection  of  the  highly- 
translucent  nuclear  membrane  shows  this  structure  to  be  a  very  tough 
viscous  solid,  and,  in  fact,  closely  allied  physically  to  the  vitelline 
membrane  and  not  at  all  the  delicate  structure  of  the  conventional 
descriptions.  With  the  exception  of  the  nucleolus,  the  nuclear  sub- 
stance is  all  in  the  sol  state.  The  nuclear  sol  is  apparently  a  homo- 
geneous liquid.  The  nucleolus  is  a  small  mass  of  quite  rigid  and 
cohesive  granular  gel  that  is  suspended  in  the  nuclear  sol. 

The  polar  body  is  a  granular,  elastic  and  highly  viscous  gel. 

In  order  to  make  it  possible  to  observe  the  structural  components 
of  the  starfish  egg  and  of  the  eggs  of  other  common  marine  inverte- 
brates, without  having  to  use  my  tedious  methods,  vital  staining  was 
resorted  to.  The  jelly  envelope  can  be  stained  a  beautiful  light  blue 
with  dimethyl-safranin-azo-dimethyl-anilin;  the  vitelline  membrane 
a  very  dark  blue  with  isamin  blue;  the  globules  or  droplets  from  yellow 
to  orange  with  vusuvin;  and  the  extremely  small  granules  a  slate  blue 
with  diethyl-safranin-azo-dimethyl-anilin. 

The  dead  or  dying  asterias  egg  shows  remarkable  morphological 
changes.  The  whole  egg  becomes  almost  opaque.  The  cytoplasm 
separates  into  a  large  number  of  more  or  less  rounded  masses  which 
still  adhere  to  each  other.  Such  masses  vary  greatly  in  size,  some 
being  as  small  as  five  microns  in  diameter.  If  the  formation  of  such 
small  masses  be  observed,  one  is  easily  misled  into  believing  that 
fusion  of  the  globules  is  occurring.  Dissection  of  such  a  mass  frees 
the  original  globules.  The  dead  gel  does  not  stick  to  a  glass  needle 
and  can  no  longer  be  drawn  out  into  strands;  it  has  lost  much  of  its 
viscidity  and  cohesiveness.  The  nuclear  fluid  has  set  and  the  result- 
ing gel  is  more  voluminous  than  was  the  nuclear  fluid  in  the  living  egg. 
The  nuclear  membrane  shows  little  change  in  its  physical  properties, 
while  the  nuclear  gel  is  elastic  and  quite  viscous  and  granular.  The 
physical  properties  of  the  dead  nuclear  gel  are  very  similar  to  those 


Physical  Properties  of  Protoplasm  155 

exhibited  by  the  living  cytoplasm.     Small  fragments  of  the  dead 
nuclear  gel  do  not  go  into  solution  when  dissected  out  in  sea  water. 


AMEBA  PROTEUS 

Small  pieces  of  ectoplasm  of  proteus  can  be  cut  off  in  distilled  water 
and  show  no  change.  This  living  substance  has  a  moderately  high 
viscosity  and  cohesiveness ;  it  does  not  stick  to  glass  needles  very 
readily  and  little  difficulty  is  experienced  in  cutting  it  into  pieces  as 
small  as  the  limit  of  microscopical  visibility.  Pieces  of  all  sizes 
appear  perfectly  homogeneous.  The  cloudiness  of  the  ectoplasmic  gel 
is  a  well-known  property.  The  inner  three  or  four  microns  of  the  hya- 
line ectoplasm  and  particularly  the  interior  of  the  outer  end  of  small 
pseudopods,  contain  varying  numbers  of  minute  granules  and  glob- 
ules that  may  measure  as  much  as  four  or  five  microns.  If  these  gran- 
ules and  globules  are  dissected  out  they  do  not  go  into  solution. 
The  globules  show  confusing  diffraction  rings ;  but,  both  globules  and 
granules  can  be  brought  out  by  light  staining  with  diethyl-safranin- 
azo-dirnethyl-anilin.  The  endoplasm  contains  a  large  contractile 
vacuole  in  which  the  presence  of  protein  has  not  been  demonstrated, 
as  yet,  and  numerous  food  vacuoles  which  contain  either  liquid  or 
liquid  and  food  masses.  The  same  kind  of  granules  and  globules 
are  found  in  the  endoplasm  as  are  found  in  the  ectoplasm  and  the 
number  of  these  structures  varies  in  different  animals.  The  sub- 
stance forming  the  walls  of  the  vacuoles  is  of  much  higher  viscosity 
and  cohesiveness.  The  living  endoplasmic  substance  is  a  very  dilute 
and  apparently  homogeneous  gel  that  possesses  a  remarkable  affinity 
for  water.  The  ectoplasm  of  ameba  then  is  a  quite  concentrated  gel 
while  the  interior  is  quite  dilute  and  is  continously  changing  its  water- 
holding  power  in  different  regions.  New  methylene  blue  R  and 
trypan  blue  are  of  great  value  in  bringing  out  the  globules,  granules 
and  vacuoles. 

The  nuclear  membrane  is  an  extremely  thin  and  moderately  tough 
solid  substance.  It  shows  some  elasticity  and  is  quite  viscous. 

The  whole  of  the  nuclear  substance  is  a  highly  rigid  and  granular 
gel,  the  minutest  pieces  of  which  show  no  appreciable  change  when 
dissected  out  in  distilled  water.  A  slight  elasticity  and  a  definite 


G.  L.  Kite 

glutinicity  are  exhibited  by  this  substance.  There  are  variations  in 
concentration  of  the  nuclear  gel  that  produce  a  characteristic  but 
misleading  optical  image.  The  nucleus  appears  to  contain  an  irregu- 
lar "network  with  granules  imbedded  in  it.  The  interstices  of  the 
network  are  very  small  luminous  spots  which  have  been  misinter- 
preted to  be  vacuoles.  Many  dissections  have  shown  that  the  granules 
are  very  concentrated  masses  of  gel;  the  network  irregularly  disposed 
masses  of  a  diluter  gel;  and  the  interstices  or  light  spots  the  most  dilute 
gel  in  the  nucleus.  The  so-called  network  is  a  part  of  the  nuclear  gel 
that  forms  a  concentration  gradient;  the  interstices  and  granules  may 
be  considered  constants  connected  by  the  grading  network.  It  should 
be  clearly  understood  that  the  network  is  not  made  up  of  definite 
threads  of  fibres  but  of  irregular  masses  of  hydrogel  that  are  very 
dense  immediately  surrounding  the  granules,  from  which  they  grade 
into  the  dilute  gel  of  the  interstices.  No  free  liquid  was  found  in  the 
nuclear  substance. 

When  the  granules  are  in  focus  they  appear  gray  and  cloudy  or 
opalescent;  when  out  of  focus  as  dark  spots.  They  measure  from 
less  than  one  to  about  two  microns  in  diameter. 

It  seems  that  a  part  of  the  luminosity  of  the  interstices  of  the 
network  is  due  to  diffraction  and  not  simply  to  slight  absorption  of 
light  by  this  portion  of  the  nuclear  substance. 

The  structural  details  of  the  nucleus  can  be  brought  out  with  con- 
siderable vividness  by  staining  with  janus  green  (diethyl-safran — in 
azo-dimethyl-anilin) . 

Slight  cuts  in  the  surface  of  proteus  qukkly  close.  Extensive 
cuts  frequently  cause  an  ameba  to  explode  —  in  as  short  a  time  as 
two  seconds  nothing  but  the  nucleus  may  remain.  If  the  contrac- 
tile vacuole  be  cut  and  its  liquid  content  caused  to  mix  with  the 
cytoplasm  the  Ameba  is  immediately  destroyed  with  explosive  vio- 
lence. A  relatively  large  dose  of  distilled  water  and  even  |  to  i 
molar  cane  sugar  solution  or  one  molar  sodium  chloride  or  potassium 
nitrate  give  a  like  result.  It  is  not  usually  possible  to  produce  more 
than  a  temporary  vacuole  with  two  molar  cane  sugar;  a  large  dose  of 
sugar  of  this  concentration  usually  causes  the  appearance  of  granules, 
globules,  fibrils  and  a  hyaline  appearance  in  any  portion  of  the  endo- 
plasm  into  which  the  injection  is  made.  The  doses  that  were  injected 
varied  from  about  270  cubic  microns  to  30,000  cubic  microns. 


Physical  Properties  of  Protoplasm  157 

A  large  number  of  indicators  have  been  injected  into  the  interior 
of  proteus  with  the  idea  of  determining  a  possible  relation  between  an 
excess  of  H+  or  OH~  ions  and  the  extraordinary  water-holding-power 
of  the  endoplasm.  Azolitmin,  sodium  alizarin  sulphonate,  tropeolin 
ooo  No.  i,  methyl  orange  and  congo  red,  dissolved  in  from  J  to  f 
molar  cane  sugar  have  been  so  far  employed.  A  neutral  to  slightly 
alkaline  reaction  is  shown  by  all  the  indicators.  It  seems  probable 
then  that  the  concomitant  variation  in  water-holding-power  of  dif- 
ferent regions  of  the  cytoplasm  is  the  mechanism  by  which  Ameba 
proteus  moves  and  is  associated  with  an  excess  of  OH~  ions. 

A  number  of  operations  were  performed  on  the  ectoplasm  of 
Ameba  proteus  for  the  purpose  of  determining  the  relation  between 
movement  and  surface  tension  changes.  The  results  of  shallow  and 
deep  cuts  in  the  ectoplasm  have  already  been  given.  The  outer  5  to  7 
microns  of  the  pseudopods  were  cut  away  in  some  animals,  and  in 
others  small  doses  of  distilled  water  were  injected  into  the  ectoplasm. 
The  removal  of  the  outer  end  of  a  pseudopod  was  usually  followed  by 
rapid  closure  of  the  incision.  The  injection  of  distilled  water  into 
the  ectoplasm  had  no  noticeable  effect  on  the  formation  of  pseudopods. 
By  means  of  such  operations  the  rigid  ectoplasm  was  either  removed, 
for  a  short  time,  from  a  given  area  of  the  surface  or  at  least  greatly 
weakened;  yet,  no  tendency  to  the  formation  of  pseudopods  was 
ever  observed,  in  such  weakened  surface  areas.  These  facts  seem  to 
justify  the  conclusion  that  surface-tension  changes  play  a  negligible 
role  in  the  movement  of  Ameba  proteus.  Furthermore,  it  may  be 
recalled,  that  the  outer  surface  of  Ameba  proteus  is  a  semi-rigid  solid 
of  from  5  to  12  or  more  microns  in  thickness,  and  it  has  still  to  be 
shown,  that  the  changes,  in  the  tension  of  the  surface  film,  that  are 
commonly  assumed  to  occur,  can  appreciably  affect  the  underlying 
semi-rigid  ectoplasm. 

The  nutrient  solution  in  which  the  amebae  were  grown  was  slightly 
alkaline  in  reaction. 

Proteus  usually  recovers  from  the  large  doses  of  neutral  salts 
and  sugar  in  much  less  than  an  hour,  almost  certainly  by  throwing 
them  off. 


158  G.  L.  Kite 


PARAMECIUM 

The  living  substance  of  Paramecium  is  a  soft,  elastic  and  somewhat 
glutinous  gel  which  can  be  drawn  out  into  strands.  It  is  filled  with  a 
large  number  of  vacuoles  of  various  sizes  the  walls  of  which  are  more 
dense  than  the  surrounding  gel.  The  surface  layer  is  more  viscous  and 
cohesive  than  the  interior.  Small  cuts  usually  close  quickly,  exten- 
sive deep  cuts  are  either  followed  by  a  loss  of  cytoplasm  or  a  rapid 
change  of  the  whole  cytoplasm  into  the  sol  state  with  almost  explosive 
violence.  If  the  fluid  in  the  contractile  vacuole  be  caused  to  mix 
with  the  cytoplasm  a  rapid  change  of  this  substance  into  the  sol  state 
results.  Suspended  in  the  living  and  apparently  homogeneous  and 
rather  dilute  gel  are  varying  numbers  of  extremely  small  granules 
and  small  globules.  Many  of  the  granules  are  recently  ingested 
bacteria.  Neither  the  granules  nor  globules  go  into  solution  when 
dissected  free  from  the  cytoplasm.  The  food  masses  are  granular 
gels  of  rather  high  viscosity. 

The  optical  properties  of  the  meganucleus  render  its  study  ex- 
tremely tedious.  It  is  almost  transparent  and  invisible.  Therefore 
its  refractive  index  and  its  dispersion  are  very  close  to  those  of  water. 
Dissection  has  proved  the  meganucleus  to  be  a  gel  of  higher  viscosity 
than  the  cytoplasm  and  to  be  slightly  glutinous  and  elastic.  The 
meganuclear  gel  has  areas,  more  dense  than  the  surrounding  sub- 
stance, that  may  be  considered  granules. 

A  complete  study  of  the  micronucleus  has  not  been  made. 


NECTURUS 

The  Striped  Muscle  Cell.  —  The.  living  substance  of  the  striped 
muscle  cell  of  Necturus  is  the  most  viscous,  elastic  and  cohesive  of 
the  living  gels  we  have  so  far  considered.  The  muscle  substance 
sticks  to  a  glass  needle  and  can  be  drawn  out  into  extraordinarily  long 
threads  which  when  released  almost  regain  their  previous  shape. 
The  absorptive  power  and  turbidity  of  this  substance  are  compara- 
tively high. 

When  the  whole  or  a  piece  of  a  muscle  cell  is  stretched  the  stria- 
tions  become  faint  or  disappear  — •  only  to  reappear  when  the  tension 


Physical  Properties  of  Protoplasm  159 

is  removed.  Beautiful  but  misleading  diffraction  phenomena  are 
to  be  observed  when  a  piece  of  muscle  cell  is  stretched.  If  the  point 
of  a  very  minute  needle  be  pushed  into  a  muscle  cell,  it  can  be  moved 
in  one  direction  about  as  easily  as  another. 

The  optical  image  of  striped  muscle  is  very  misleading.  Dissec- 
tions have  shown  that  the  dark  bands  seen  in  living  muscle  are  pro- 
duced by  concentrated  areas  of  muscle  substance  which  absorb  enough 
transmitted  light  of  low  intensity  to  appear  as  dark  bands  in  the 
optical  image.  I  have  been  unable  to  dissect  out  definite  fibrils. 
The  substance  lying  between  the  concentrated  regions  and  appearing 
as  light  bands  is  a  highly  viscous,  elastic  gel  and  has  no  physical 
properties  that  serve  to  distinguish  it  from  the  surrounding  sarco- 
plasmic  gel.  By  cutting  the  dark  band  to  pieces,  small  masses  of 
highly  concentrated  muscle  substance,  frequently  less  than  one 
micron  in  diameter,  are  partially  freed  from  the  dilute  enveloping 
gel  and  in  light  of  low  intensity  show  well-defined  diffraction  halos. 
The  appearance  of  dark  bands  in  the  optical  image,  then,  is  produced 
by  absorption  of  light  waves  by  the  concentrated  muscle  substance; 
the  light  bands,  by  the  low  absorptive  power  of  the  diluter  inter- 
mediate gel,  and  the  diffraction  of  the  light  waves  by  the  edges  of  the 
concentrated  substance.  Striking  changes  in  the  optical  image  that 
are  well  known  can  be  produced  by  increasing  the  intensity  of  illumi- 
nation. The  dark  band  becomes  cloudy  and  more  or  less  opalescent 
and  the  light  band  may  show  an  intersecting  dark  line  or  well-defined 
diffraction  fringes  just  outside  the  geometrical  shadow  of  the  con- 
centrated substance.  Hence,  absorption,  diffraction,  refraction  and 
dispersion  are  involved  in  the  formation  of  the  optical  image  of  striped 
muscle  and  the  former  two  particularly  when  the  illumination  is  of  a 
relatively  high  intensity. 

The  nuclear  substance  is  a  gel  that  is  for  the  most  part  compara- 
tively dilute  but  contains  more  concentrated  areas  in  the  form  of 
granules  and  an  imperfect  network.  The  appearance  of  a  network 
in  the  optical  image  is  due  not  to  definite  fibrils  but  to  more  con- 
centrated parts  of  the  gel  that  grade  into  the  diluter  nuclear  substance. 

On  the  outer  surface  of  the  muscle  cell  is  found  a  highly  trans- 
lucent membrane,  the  sarcolemma,  which  is  extremely  elastic  and 
measures  about  one  micron  in  thickness.  It  is  stuck  to  the  whole 
outer  surface  of  the  muscle  cell  and  is  viscous  and  cohesive  enough 


160  G.  L.  Kite 

to  offer  an  appreciable  resistance  to  a  glass  needle  a  micron  or  less  in 
diameter.  The  disagreement  among  investigators  concerning  the 
presence  of  a  sarcolemma  is  due  to  the  fact  that  it  is  transparent  and 
that  its  refractive  and  dispersive  powers  are  so  nearly  the  same  as 
those  of  water.  Instead  of  being  the  delicate  structure  of  the  con- 
ventional descriptions,  the  sarcolemma  of  the  striped  muscle  cell  of 
Necturus  exhibits  physical  properties  that  are  very  similar  to  those  of 
the  vitelline  membrane  of  an  echinoderm  egg. 

If  a  concentrated  solution  of  isamin  blue  made  by  boiling  in  dis- 
tilled water  or  .8  per  cent  sodium  chloride  be  added  to  freshly  teased 
muscle  cells,  blue  staining  of  the  sarcolemma  occurs  in  ten  to  fifteen 
minutes. 

An  Epidermal  Cell.  —  The  epidermal  cells  are  embedded  in  an 
intercellular  gel  of  extremely  high  viscosity  and  considerable  elas- 
ticity. The  substance  is  tough  but  softer  than  many  nuclear  mem- 
branes and  shows  a  relatively  high  absorptive  power.  It  is  also  quite 
turbid.  A  few  globules  and  granules,  varying  in  size  from  about 
one  to  four  microns,  that  can  be  easily  stained  with  diethyl-safranin- 
azo-dimethyl-anilin  are  to  be  seen  scattered  through  the  intercellular 

gel- 

The  whole  cell  substance  is  a  gel  of  even  higher  rigidity  than  the 
muscle  substance  of  the  same  animal.  Small  pieces  cut  out  of  the 
nucleus  or  cytoplasm,  in  distilled  water  or  .8  per  cent  sodium  chloride, 
show  no  appreciable  change. 

The  cytoplasm  exhibits  a  high  absorptive  power  and  a  definite 
elasticity.  Very  small  granules  that  seem  to  be  denser  cytoplasmic 
areas  are  to  be  seen  scattered  throughout  the  turbid  cytoplasm. 
Many  cells  show  radially  arranged  fibrils,  in  the  outer  part  of  the 
cytoplasm,  which  can  be  partially  freed  from  the  surrounding  gel  by 
dissection.  Such  a  fibril  is  physically  and  optically  more  dense  than 
the  remainder  of  the  cytoplasm. 

The  nuclear  membrane  is  thin,  clear,  and* quite  cohesive  and  elas- 
tic, and  1ms  a  different  index  of  refraction  from  the  cytoplasm  and 
nucleus. 

The  nuclear  gel  is  of  a  higher  viscosity  than  the  cytoplasm.  The 
appearance  of  a  network  in  the  optical  image  of  the  nucleus  is  due  to 
concentrated  areas  in  the  form  of  granules  and  imperfect  threads  which 
are  not  sharply  separated  from,  but  grade  into,  the  surrounding  diluter 


Physical  Properties  of  Protoplasm  161 

gel.     The  whole  nuclear  substance  is  quite  glutinous.     No  trace  of 
free  liquid  could  be  found  in  the  nucleus. 


SPIROGYRA 

The  cellulose  wall  of  Spirogyra  is  enormously  cohesive;  it  is  cut 
or  punctured  with  extremely  fine  Jena  glass  needles  with  considerable 
difficulty.  The  outer  surface  is  covered  by  an  almost  invisible  soft 
gel,  that  frequently  measures  five  or  more  microns  in  thickness  and 
can  be  stained  red  with  sodium  alizarin  sulphonate  in  a  neutral  or 
slightly  alkaline  solution.  A  layer  of  dilute  granular  gel  covers  the 
inner  surface  of  the  cellulose  wall  and  is  connected  by  a  number  of 
strands  of  an  elastic  gel  to  a  central  mass  of  living  substance,  in  which 
a  small  nucleus  is  imbedded.  The  central  mass  of  gel  contains  a 
few  granules  and  is  of  a  higher  viscosity  and  cohesiveness  than  the 
surface  cytoplasm.  This  mass  also  has  a  higher  refractive  index  and 
higher  absorptive  power  than  the  surface  cytoplasm.  The  anchoring 
strands  of  gel  decrease  in  viscosity  from  within  outwards.  Much 
of  the  surface  layer  of  cytoplasm  is  usually  invisible.  Hence,  it  is 
quite  translucent  and  has  refractive  and  dispersive  powers  very  close 
to  those  of  water.  If  the  cell  wall  be  cut  across  the  surface  cytoplasm 
shrinks.  The  chloroplasts  either  shrink  or  separate  into  rounded 
masses.  The  chloroplasts  have  a  higher  viscosity  and  elasticity  than 
the  gel  in  which  they  are  imbedded. 

The  pyrenoid  is  a  complex  structure.  Dissection  shows  the 
presence  of  an  optically  dense  but  fragile  wall  which,  when  broken, 
frees  a  globule  that  is  of  considerable  interest.  This  globule  shows 
many  of  the  optical  properties  of  an  oil  droplet  but  has  too  high  a 
viscosity  to  round  up  under  the  influence  of  surface  tension;  there- 
fore it  seems  to  be  a  true  gel. 

None  of  the  cytoplasm  goes  into  solution  very  readily  even  when 
cut  into  very  minute  pieces. 

The  nucleus  of  Spirogyra  is  a  gel  that  has  higher  viscosity  and 
refractive  and  absorptive  powers  than  the  cytoplasm.  It  is  also 
more  cloudy  than  the  cytoplasm.  There  are  denser  areas  in  the 
nuclear  substance  in  the  form  of  granules  and  threads  that  form  a 
sort  of  network.  Small  pieces  dissected  from  all  parts  of  the  nucleus 


162  G.  L.  Kite 

into  water,  not  only  do  not  go  into  the  sol  state  but  remain  too  rigid 
to  show  surface  tension  effects.  Pieces  of  broken  glass  needles  stick 
firmly  to  the  nuclear  gel  when  imbedded  in  it.  The  image  of  the 
nucleus  is  false  in  important  details.  The  denser  areas,  when  in  the 
focal  plane,  appear  as  grayish  or  slightly  opalescent .  granules  and 
threads  and  when  above  or  below  the  focal  plane  as  dark  spots 
and  lines.  Besides,  if  the  intensity  of  the  illumination  be  increased 
the  network  appears  much  finer.  Very  small  dense  masses  of  gel 
could  be  partly  freed  from  the  remaining  nuclear  substance.  It 
seems  proper  to  term  such  structures  granules.  On  the  other  hand, 
the  dense  masses  that  produce  the  appearance  of  a  network  in  the 
image  are  not  actual  threads  that  are  sharply  separated  from  the 
surrounding  gel  but  irregularly  shaped  dense  areas  that  grade  into 
the  immediately  contiguous  diluter  gel.  The  light  spots  that  change 
their  position  at  different  focal  planes  seem  to  be  due  chiefly  to 
two  factors,  viz.,  a  relatively  low  absorptive  power  of  the  gel 
occupying  the  interstices  of  the  network  and  diffraction  by  the  edges 
of  the  denser  areas. 

It  seems  certain  that  the  vacuolar  fluid  of  Spirogyra  contains 
protein  and  must  be  considered  a  hydrosol.  Much  evidence  has 
been  adduced  in  support  of  this  statement.  A  number  of  injections 
of  Millon's  fluid  into  the  vacuole  were  made  with  positive  results. 
Extremely  small  solid  particles  appeared  in  the  cell  sap  after  the 
injection  of  such  precipitating  agents  for  proteins,  as  saturated  subli- 
mate, 40  per  cent  formaldehyde,  saturated  picric  acid  and  saturated 
phosphotungstic  acid  containing  5  per  cent  sulphuric  acid. 

The  vacuolar  fluid  is  cloudy.  This  is  positive  proof  of  the  pres- 
ence of  ultramicroscopic  particles  which  would  ordinarily  be  con- 
sidered protein  even  in  the  absence  of  a  positive  color  test  for  protein. 

The  cell  sap  of  Chara  seems  to  be  richer  in  protein  than  that  of 
Spirogyra.  This  conclusion  is  based  on  the  fact  that  a  compara- 
tively heavy  precipitate  results  from  the  in tra vacuolar  injection  of 
saturated  sublimate  or  40  per  cent  formaldehyde.  Hence,  it  is  proba- 
ble that  cell  sap  containing  protein  is  very  common  in  plants. 

Mucor,  Saprolegnia,  Hydrodictyon,  Chara  and  the  parenchymatous 
cells  of  the  leaves  of  Tradescantia  have  been  dissected  for  comparison 
with  animal  cells.  In  general,  it  may  be  stated  that  the  cellulose 
walls  of  plants  are  extremely  cohesive  and  are  cut  and  punctured 


Physical  Properties  of  Protoplasm  163 

with  considerable  difficulty.     The  protoplasm  of  plant  cells  is  much 
more  dilute  or  less  rigid  than  that  of  animal  cells. 


RESTING  AND  DIVIDING  MALE  GERM  CELLS  OF  THE  SQUASH 
BUG  (ANASA).    GRASSHOPPERS  AND  CRICKETS 

A  brief  note  has  been  published  on  this  subject.21 

The  whole  cell  substance  of  resting  and  dividing  spermatogonia 
and  spermatocytes  is  a  moderately  viscous  gel.  Cutting  away  pieces 
of  the  cytoplasm  and  nucleus  in  Ringer's  fluid  shows  that  these  struc- 
tures are  far  too  rigid  to  flow  or  change  shape  under  such  experi- 
mental treatment.  The  appearance  of  a  network  is  due  to  denser 
masses  of  nuclear  gel  that  grade  into  the  diluter  surrounding  substance. 
No  definite  threads  or  fibrils  could  be  dissected  out  of  resting  nuclei. 
Some  of  the  optical  principles  involved  in  a  study  of  the  living  nuclei 
of  spermatogonia  and  spermatocytes  were  discussed  in  connection 
with  the  nucleus  of  proteus. 

Very  definite  statements  can  be  made  about  the  physical  proper- 
ties of  chromosomes  and  spindle  fibres.  The  chromosome  has  been 
found  to  be  the  most  highly  concentrated  and  rigid  part  of  the  nuclear 
gel.  Such  a  mass  of  gel  is  less  translucent  and  has  a  higher  refractive 
index  and  absorptive  power  than  the  diluter  homogeneous  gel  in  which 
it  is  imbedded.  A  chromosome  when  dissected  out  shows  no  affinity 
for  water  and  does  not  disintegrate  readily.  tPieces  of  it  stick  to  the 
glass  dissecting  needle  but  when  drawn  out  show  no  marked  elas- 
ticity. The  spindle  fibre  is  an  elastic  concentrated  thread  of  nuclear 
gel  and  its  absorptive  power  and  refractive  index  are  also  different 
from  those  of  the  diluter  gel  in  which  the  spindle  fibre  is  imbedded 
and  from  which  it  cannot  be  entirely  freed.  Metaphase  spindle  fibres 
that  were  dissected  out  with  great  care  seemed  continuous  with  the 
ends  of  the  chromosomes.  The  homogeneous  gel  in  which  a  telophase 
spindle  is  imbedded  is  so  rigid,  that  all  the  surrounding  cytoplasm 
can  be  cut  away  and  the  spindle  and  chromosomes  show  no  appreciable 
change;  metaphase,  anaphase  and  telophase  spindles  can  be  cut  to 
pieces  in  Ringer's  fluid  and  the  pieces  are  so  rigid  that  they  undergo 
no  change  in  shape. 

21  KITE  and  CHAMBERS:  1912,  Science,  N.  S.,  xxxvi,  p.  639. 


1 64  G.  L.  Kite 

Many  of  the  physical  and  chemical  changes  of  cell-division  are 
reversible.  Pressure  on  the  cell  plate  of  spermatocytes  in  telophase 
has  caused  rapid  fusion  of  the  daughter  cells  and  extensive  swelling 
and  loss  in  rigidity  of  the  protoplasmic  gel  in  which  the  spindle  fibres 
are  imbedded.  If  the  displaced  spindle  fibres  and  chromosomes  are 
dissected  out,  after  such  a  partial  reversal,  they  are  found  to  have 
undergone  no  appreciable  change  in  rigidity. 

From  a  preliminary  study  of  mitosis,  a  few  conclusions,  that  are 
probably  general,  can  be  drawn.  It  seems  that  cell-division  results 
primarily  from  concomitant  shrinking  and  swelling  or  change  in  water- 
holding-power  of  different  portions  of  the  cell  protoplasm.  Many  of 
the  structural  elements  of  the  mitotic  figure  separate  out  of  the  pro- 
toplasm and  change  in  rigidity  according  to  their  water-content. 
During  the  prophase,  the  nuclear  substance  becomes  so  soft  that 
movement  of  the  components  of  the  nucleus  is  affected  by  flowing 
of  the  nuclear  gel.  The  mechanism  at  the  basis  of  this  flowing  seems 
to  be  a  change  in  water-holding-power  of  the  nuclear  components. 

I  wish  here  to  thank  Dr.  A.  P.  Mathews  for  the  very  helpful 
interest  that  he  has  shown  in  this  investigation. 


Reprinted  from  THE  JOURNAL  OF  BIOLOGICAL  CHEMISTRY.  VOL.  XIV,  No.  2,  1913 


ON  THE  NATURE  OF  THE  IODINE-CONTAINING 
COMPLEX  IN  THYREOGLOBULIN. 

BY  FRED  C.  KOCH. 

(From  the  Hull  Laboratories  of  Biochemistry  and  Pharmacology,  University 

of  Chicago.} 

(Received  for  publication,  January  27,  1913.) 

In  this  paper  are  given  the  results  of  an  attempt  to  determine 
the  nature  of  the  active  complex  in  the  iodine-containing  active 
principle  of  the  thyroid  gland.  Although  the  nature  of  this  group 
was  not  determined,  the  quantitative  physiological  results  here 
reported  serve  to  establish  certain  predicted  and  other  unexpected 
facts  and  to  eliminate  certain  hitherto  considered  probabilities. 

The  problem  was  taken  up  both  by  analytical  and  by  synthetic 
methods.  In  the  former  method  the  physiological  activity  and 
iodine  content  of  the  dried  thyroid  tissue,  the  globulin  therefrom 
and  various  products  of  hydrolysis  from  this  globulin  were  deter- 
mined quantitatively.  In  the  second  method  two  iodized  amino- 
acid  derivatives,  not  previously  tested  by  quantitative  methods, 
were  prepared  synthetically  and  their  physiological  activity  stud- 
ied quantitatively. 

In  thus  tracing  the  active  complex  a  number  of  important  as- 
sumptions were  made.  First,  that  the  activity  of  unaltered  thy- 
roid tissue  depends  quantitatively  on  its  iodine  content.  Second, 
that  the  best  method  known  for  measuring  this  activity  directly 
and  quantitatively  is  the  Reid  Hunt  acetonitrile  test.1  Third, 
that  in  case  the  iodine  is  present  in  the  products  of  hydrolysis  in 
the  same  combination  as  in  the  globulin  then,  per  unit  of  iodine, 
these  will  still  possess  an  activity  comparable  with  the  original 
globulin.  Fourth,  that  in  case  the  iodine  complex  is  an  iodized 
amino-acid  and  that  in  case  this  is  decomposed  in  the  process  of 
hydrolysis  then  the  synthetic  preparation  of  various  iodized 
amino-acids  or  derivatives  thereof  and  the  quantitative  testing  of 

1  This  Journal,  i,  p.  33,  1905. 


THE   JOURNAL   OF   BIOLOGICAL  CHEMISTRY,    VOL.    XIV,    NO.    2. 


102        The  Iodine  Complex  of  Thyreoglobulin 

these  per  unit  of  iodine  may  determine  the  probable  nature  of  the 
iodine  complex.  In  other  words,  the  actual  quantitative  physio- 
logical activity  per  unit  of  iodine  as  measured  by  the  Reid  Hunt 
method  was  taken  as  the  crucial  test  for  the  presence  or  absence 
of  the  unaltered  iodine  complex. 

The  historical  development  of  the  relation  of  thyroid  activity 
to  iodine  content  need  not  be  considered  at  this  time,  especially 
in  view  of  the  thorough  reviews  and  extensive  confirmatory  experi- 
ments made  by  Reid  Hunt  and  A.  Seidell,2  as  well  as  the  compara- 
tive histological  and  chemical  studies  by  Marine  in  cooperation 
with  Lenhardt  and  Williams.3  A  careful  study  of  these  papers 
justifies  the  first  assumption.  The  second  assumption  is  also 
well  taken  provided  the  proper  precautions  are  observed  as  shown 
by  Reid  Hunt  and  A.  Seidell.4  Other  methods  for  testing  the 
physiological  activity  of  thyroid  substance,  based  on  changes  in 
blood  pressure,5  on  increasing  the  irritability  of  the  depressor 
nerve,6  on  changes  in  nitrogen  metabolism7  and  on  curative  effects 
in  cretinism8  have  been  employed,  but  are  not  applicable  in  a 
quantitative  study,  nor  are  they  as  specific  reactions. 

Of  the  third  and  fourth  assumptions  we  had  no  definite  proof. 
The  studies  of  Oswald9  and  others  show  that  during  hydrolysis 
of  thyreoglobulin  only  30  per  cent  or  less  of  the  iodine  remains 
in  organic  combination.  The  iodine  thus  combined  is  in  the  vari- 
ous fractions  and  qualitatively  it  has  been  determined10  that  prob- 
ably the  greater  activity  remains  in  the  more  complex  products 

2  Bulletins  47  (1908)  and  69  (1910)  of  the  Hygienic  Laboratory,  U.  S.  Pub- 
lic Health  and  Marine  Hospital  Service. 

3  Johns  Hopkins  Hospital  Bull,  xviii,  p.  359,  1907;  Journ.  Inf.  Dis.,  iv, 
p.  417,  1907;  Archives  of  Internal  Med.,  i,  p.  349,  1908;  Ibid.,  iii,  p.  66,  1909; 
ibid.,  iv,  p.  440,  1909;  ibid.,  vii,  p.  506,  1911;  ibid.,  viii,  p.  265,  1911; 
Journ.  of  Exp.  Med.,  xiii,  p.  455,  1911. 

4  Loc.  cit.;  Journ.  of  Pharmacol.  and  Exp.  Ther.,  ii,  p.  15,  1910. 

5  von  Fiirth  and  Schwarz:  Pfluger's  Archiv,  cxxiv,  p.  113,  1908. 

6  von  Cyon  and  Oswald:  Pfliiger's  Archiv,  Ixxxiii,  p.  199, 1901;  Asher  and 
Flack:  Zeitschr.  f.  Biol,  Iv,  p.  83,  1910. 

7  Baumann:  Zeitschr.  f.  physiol.  Chem.,  xxi,  p.  487,  1896;  ibid.,  xxii,  p.  1, 
1896;  Munch,  med.  Wochenschr.,  xl,  1896. 

8  E.  Pick  and  F.  Pineles:  Zeitschr.  f.  exp.  Path.  u.  Ther.,  vii,  p.  518,  1909- 
10. 

9  Arch.f.  exp.  Path.  u.  Pharm.,  Ix,  p.  115,  1908. 

10  Pick  and  Pineles:  loc.  cit. 


Fred  C.  Koch  103 

of  hydrolysis  where  also  the  greater  part  of  the  organically  com- 
bined iodine  is  found.  What  relation  the  activity  bears  to  the 
iodine  content  therein  has  however  not  been  determined.  As 
stated  above  we  have  evidence  that  some  of  the  iodine  is  split 
off  as  iodide,  but  we  have  no  direct  evidence  that  all  the  organ- 
ically combined  iodine  found  in  the  products  of  hydrolysis  is  still 
in  the  same  complex  or  in  the  same  structural  relationship  as  in  the 
original  thyreoglobulin.  A  number  of  iodized  amino-acids  have 
been  studied  qualitatively  as  to  physiological  activity.  In  no 
case  has  thyroid  activity  been  detected.  The  most  conclusive 
results  as  to  the  inactivity  of  3,5-iodo-laevo-tyrosine  are  those 
reported  by  Strouse  and  Voegtlin.11  Other  observations  on  the 
inactivity  of  various  iodized  proteins,  which  on  hydrolysis  yield 
3,5-iodo-tyrosine,  also  bear  out  these  conclusions.  The  studies 
on  other  iodized  amino-acids  do  not  lead  to  definite  conclusions. 
Thus  von  Fiirth  and  Schwarz12  prepared  and  studied  what  they  con- 
sidered iodized  phenylalanine,  histidine  and  tryptophane.  They 
reported  all  these  substances  as  physiologically  inactive,  but  gave 
no  data  indicating  that  they  had  really  separated  iodo-deriva- 
tives  of  these  substances.  Pauly13  however  actually  separated 
pure  tetra-iodohistidine  anhydride  and  tri-iodo-imidazol  and  re- 
ported that  these  substances  increased  the  respiratory  and  pulse 
frequencies,  although  uniodized  imidazol  had  no  such  action. 
These  considerations  lead  us  to  conclude  that  for  the  present  the 
validity  of  the  third  and  fourth  assumptions  is  unknown  to  us  and 
that  the  true  answers  thereto  are  part  of  the  problem  in  hand. 

EXPERIMENTAL    PART. 

The  mode  of  attack  has  already  been  outlined  above.  The 
details  as  to  the  methods  employed  and  the  preparation  of  the 
substances  studied  are  given  below. 

A.  Preparations. 

Dried  hog  thyroids.  Hog  thyroids14  were  freed  mechanically  from  fat 
as  much  as  possible  and  dried  on  glass  plates  in  a  current  of  air  at  30-35 °C. 

11  Journ.  ofPharm.  andExp.  Ther.,  i,  p.  123,  1909. 

12  Pfliiger's  Archiv,  cxxxiv,  p.  113,  1908. 

13  Ber.  d.  deutsch.  chem.  Gesellsch.,  xliii,  p.  2243,  1910. 

14  The  raw  material  for  this  research  was  supplied  by  the  Armour  Labora- 
tory Department. 


104 


Iodine  Complex  of  Thyreoglobulin 


The  mass  was  then  ground  to  a  coarse  powder  and  fat  removed  by  ether  in 
the  cold.  The  remaining  dry  mass  was  then  finely  powdered.  Duplicate 
determinations  on  this  gave  0.243  and  0.250  per  cent  iodine. 

Thyreoglobulin.  This  was  prepared  as  previously  described.15  Dupli- 
cate determinations  on  this  gave  0.462  and  0.468  per  cent  iodine. 

lodothyrin  (a)  was  prepared  by  the  usual  Baumann  process  from  the  above 
thyreoglobulin.  The  extraction  with  95  per  cent  alcohol  of  the  melanoidin 
precipitate  was  made  in  a  continuous  hot  extractor.  Duplicate  determina- 
tions gave  5.81  and  5.85  per  cent  iodine. 

lodothyrin  (6)  was  obtained  in  the  same  way  from  the  melanoidin  precipi- 
tate which  separated  in  the  complete  hydrolysis  of  some  of  the  same  thyreo- 
globulin by  30-35  per  cent  sulphuric  acid.  This  on  analysis  gave  7.51  per 
cent  iodine. 

lodothyrin  (c)  was  obtained  from  40  grams  of  the  same  globulin  by  hydroly- 
sis for  three  days  at  room  temperature  and  for  twenty-four  hours  at  boil- 
ing temperature  with  20-25  per  cent  phosphoric  acid.  Phosphoric  acid 
was  used  as  it  was  thought  that  possibly  the  oxidative  action  of  sulphuric 
acid  might  have  an  injurious  effect.  This  amount  of  globulin  yielded  3.30 
grams  of  melanoidin,  containing  1.75  per  cent  iodine.  The  iodothyrin 
extracted  from  this  represented  24  per  cent  of  the  weight  and  contained  4.44- 
4.46  per  cent  iodine.  Thus  only  61  per  cent  of  the  iodine  in  the  melanoidin 
fraction  was  recovered  in  the  alcohol  extract. 

Metaprotein  (A4).  The  nitrate  from  the  melanoidin  fraction  above  was 
neutralized  with  NaOH  and  the  metaprotein  separated  and  dried  over  sul- 
phuric acid  in  a  vacuum  desiccator.  This  weighed  1 .62  grams  and  contained 
1.51-1.53  per  cent  iodine. 

Primary  albumose  (A6).  The  filtrate  from  above  was  half  saturated  with 
zinc  sulphate  after  slightly  acidifying  with  sulphuric  acid.  The  precipitate 
obtained  was  dialyzed  until  free  from  sulphate.  In  this  fraction  there  were 
recovered  3.1  grams  containing  0.22-0.225  per  cent  iodine. 

Secondary  albumose  (A6).  Obtained  from  the  filtrate  from  above  by  com- 
plete saturation  with  zinc  sulphate.  The  precipitate  after  dialyzing  as 
above  yielded  4  grams  dry  substance  containing  0.069  per  cent  iodine. 

The  table  (I)  below  gives  a  summary  of  the  distribution  of  iodine  in  the 
different  fractions  above. 

TABLE  I. 


WEIGHT 
KBCOVERED 

PER  CENT  OF 
IODINE 
THEREIN 

WEIGHT  OF 
IODINE 

PER  CENT  OF 
TOTAL  IODINE 
IN  THE 
GLOBULIN 

Melanoidin  precipitate 
Metaprotein  

3.30 
1  62 

1.74 
1  52 

0.0575 
0  0246 

30.9 
13  2 

Primary  albumose  
Secondary  albumose.  .  . 
Undetermined  iodine  .  . 

3.01 
4.0 

0.22 
0.0695 

0.0066 
0.0027 

3.5 
1.5 
50.9 

15  This  Journal,  ix,  p.  121,  1911. 


Fred  C.  Koch  105 

Phosphotungstic  acid  precipitate.  Another  40  grams  of  thyreoglobulin 
were  boiled  with  25  per  cent  phosphoric  acid  for  ninety-three  hours.  The 
filtrate  from  the  melanoidin  precipitate  and  metaprotein,  after  removal  of 
the  phosphoric  acid  by  Ba(OH)2  and  the  excess  of  barium  by  sulphuric  acid, 
was  concentrated  under  diminished  pressure  to  about  250  cc.  This  was 
then  freed  from  proteose  and  peptone  by  the  Kutscher  tannin  method.16 
The  filtrate  finally  obtained  here  after  removal  of  the  excess  of  lead  was 
boiled  with  BaCO3  to  remove  the  ammonia.  The  dissolved  barium  was 
again  removed  by  sulphuric  acid.  The  filtrate  after  acidifying  with  H2SO4 
to  5  per  cent  strength  was  precipitated  with  phosphotungstic  acid  in  the 
usual  way.  The  precipitate  after  thorough  washing  with  2.5  per  cent  phos- 
photungstic acid  solution  was  freed  from  phosphotungstic  acid,  barium  and 
sulphate  in  the  usual  way.  Duplicate  determinations  on  the  dry  amino- 
acid  mixture  gave  0.0107  per  cent  and  0.0093  per  cent  iodine. 

Another  phosphotungstic  acid  precipitate  from  a  hydrolysis  by  H2SO4 
was  worked  up  in  the  same  way.  This  dry  residue  contained  0.0068  per  cent 
iodine.  The  two  samples  were  mixed  and  designated  as  P.T.A.  Ppt.  1. 
This  mixture  contained  0.0073  per  cent  iodine. 

Phosphotungstic  acid  filtrate  (1).  This  was  freed  from  phosphotungstic 
acid  in  the  usual  way.  The  amino-acid  solution  was  evaporated  to  dryness. 
Duplicate  determinations  on  the  dry  amino-acid  mixture  gave  0.0024  per 
cent  iodine. 

Phosphotungstic  acid  precipitate  (2) .  This  was  obtained  in  the  same  way 
as  the  above  from  the  partial  hydrolysis  by  10  per  cent  sulphuric  acid  of 
141. 6  grams  of  thyreoglobulin  containing  0.511  per  cent  iodine.  The  puri- 
fied dry  residue  by  analysis  contained  0.0043  per  cent  iodine. 

Phosphotungstic  acid  filtrate  (2}.  The  filtrate  from  the  above  was  treated 
in  the  usual  way.  The  dry  purified  amino-acid  mixture  left  gave  in  dupli- 
cate determinations  0.0045  and  0.0043  per  cent  iodine. 

Tetra-iodohistidine  anhydride.  Histidine  was  prepared  from  ox  erythro- 
cytes  by  the  method  of  Frankel.17  Various  methods  were  employed  in 
trying  to  iodize  the  dichloride  or  the  base  itself  but  in  no  case  were  there 
indications  of  true  absorption  of  iodine,  but  rather  decomposition  of  the 
histidine.  While  this  work  was  under  way  Pauly18  published  his  obser- 
vations with  the  same  conclusions  as  to  the  difficulty  or  inability  to  iodize 
histidine  directly.  At  the  same  time,  as  stated  above,  he  published  his 
observations  on  tetra-iodohistidine  anhydride.  Following  the  methods 
given  by  Pauly19  the  preparation  of  the  methyl  ester  of  histidine  dichloride 
was  carried  out  and  from  this  the  histidine  anhydride  by  the  Pauly 
modification20  of  the  Fischer  and  Zuzuki  method.  The  histidine  anhydride 
was  recrystallized  from  hot  water  a  number  of  times  to  obtain  the  more 

"Zentralbl.  f.  PhysioL,  xix,  p.  504,  1905. 

17  Monatsh.f.  Chem.,  xxiv,  p.  230,  1903. 

18  Ber.  d.  deutsch.  chem.  Gesellsch.,  xliii,  p.  2243,  1910. 

19  Zeitschr.  f.  physiol.  Chem.,  Ixiv,  p.  75,  1910. 

20  Loc.  cit. 


io6        The  Iodine  Complex  of  Thyreoglobulin 

readily  soluble  laevorotatory  form.  This  was  then  iodized  according  to 
the  Pauly  method.  One  determination  on  the  snow-white  product  gave  63 
per  cent  iodine  (theoretical  65  per  cent).  The  slightly  lower  value  may 
be  due  to  an  admixture  of  a  small  amount  of  di-iodohistidine  anhydride. 

Iodized  tryptophane.  Tryptophane  was  prepared  from  commercial  casein 
by  the  Hopkins-Cole  method.21  Several  attempts  were  made  to  iodize 
the  pure  crystals  by  the  method  of  Neuberg,22  but  in  no  case  was  a  substance 
obtained  containing  more  than  6.3  per  cent  iodine.  The  preparation  finally 
made  for  physiological  testing  was  obtained  by  dissolving  one  milligram 
molecule  of  tryptophane  in  4  cc.  of  |  NaOH,  cooling  by  immersing  in  ice 
water  and,  while  keeping  cool  and  stirring  well,  adding  drop  by  drop  6  cc. 
of  aqueous  N  iodine  solution.  The  mixture  was  allowed  to  stand  at  ice  box 
temperature  for  twenty-four  hours,  then  filtered  off.  The  precipitate  was 
well  washed  with  cold  water  and  dried  over  sulphuric  acid  in  a  vacuum  desic- 
cator. The  product  obtained  is  light  brown  in  color,  readily  soluble  in  alka- 
lies, reprecipitated  on  acidifying  and  liberates  a  very  small  amount  of  iodine 
to  chloroform  on  shaking  therewith.  Duplicate  determinations  on  this 
gave  41.5  and  41.9  per  cent  iodine  (the  theoretical  for  mono-  and  di-iodo- 
tryptophane  are  38.4  per  cent  and  55.7  per  cent  respectively). 

B.  Methods. 

Determination  of  iodine.  The  Hunter23  method  with  slight  modifications 
was  employed.  The  material  to  be  analyzed,  taken  in  quantities  of  0.05- 
2  grams  was  mixed  with  15  grams  of  fusion  mixture  and  covered  with  10 
grams  of  fusion  mixture  as  suggested  by  Hunter.  To  conduct  the  fusion  the 
Roger's  ring  burner  was  found  to  be  much  more  satisfactory  in  ensuring  a 
uniform  rapid  heating  without  overheating.  With  the  size  of  the  flame  once 
determined  one  "finds  ten  minutes  to  be  ample  time  to  give  a  satisfactory, 
easily  removable  fusion.  In  the  treatment  with  alkaline  hypochlorite  it 
was  considered  best  to  warm  to  40°C.  for  ten  minutes.  In  acidifying  it  is 
very  important  to  make  sufficiently  acid  and  then  always  to  the  same  degree. 
Sulphuric  acid  of  25  per  cent  strength  was  used  here  and  since  the  same 
amounts  of  fusion  mixtures  and  hypochlorite  were  used  in  each  case  the 
acidity  was  well  controlled  by  always  adding  the  same  amount  of  acid. 
In  removing  the  excess  of  chlorine  gentle  boiling  was  continued  for  forty 
minutes  after  the  negative  test  of  the  vapors  by  starch  iodine  paper.  In 
this  way  the  blank  test  on  the  reagents  never  was  more  than  0.1  cc.  of  a 
^  Na2S2O3.5H2O  solution. 

Physiological  testing  by  the  Hunt  method.  The  method  employed  was  that 
of  feeding  the  same  quantity  of  iodine,  in  the  different  combinations,  to 
white  mice  in  such  a  manner  as  to  make  as  certain  as  possible  the  entire 
consumption  of  the  material  fed.  In  order  to  do  this  each  mouse  was  first 

21  Journ.  of  PhysioL,  xxvii,  p.  418,  1901. 

22  Biochem.  Zeitschr.,  vi,  p.  276,  1907. 

23  This  Journal,  vii,  p.  321,  1910. 


Fred  C.  Koch  107 

fed  for  three  or  f  >ur  days  with  cracker  dust  made  into  pellets  of  known 
weight.  At  the  close  of  this  preliminary  feeding  the  unconsumed  material 
was  weighed  and  from  this  the  average  amount  eaten  per  day  determined. 
For  ten  days  following  this  period  each  mouse  then  received  this  weight 
of  cracker  dust,  with  the  incorporated  iodine-containing  substance,  in 
the  form  of  pellets.  The  control  mice  were  fed  in  the  same  way  with 
plain  cracker  dust  pellets.  At  the  end  of  the  10-day  feeding  period  the 
acetonitrile  was  injected  subcutaneously.  Each  dose  administered  in 
series  I,  II  and  III  was  contained  in  1  cc.  of  fluid;  in  series  IV-IX,  in  0.5 
cc.;  in  series  X,  in  0.66  cc.  In  most  cases  the  animals  consumed  the  food 
very  well.  All  the  mice  used  were  raised  in  the  laboratory  building  on  a 
diet  of  milk  and  crackers  with  occasional  bits  of  lettuce  until  used  for  the 
experiment.  Care  was  taken  to  compare  mice  of  as  nearly  the  same  age  as 
possible.  In  the  tables  below  the  litter  number  of  each  mouse  is  given. 
The  ages  of  the  mice  of  the  various  litters  were  as  follows :  Litter  2, 119  days; 
litter  3, 102  days;  Utter  4,  100  days;  litter  5,  80  days;  litters  6  and  10,  99  and 
113  days  respectively;  litter  9,  115  days;  litters  11-12,  125  and  135  days 
respectively;  litters  13-14,  144  and  151  days  respectively;  litter  28,  85  days; 
litters  29-30,  59  and  66  days  respectively;  litters  31,  32  and  34,  95,  85  and  97 
days  respectively;  litters  33-35, 101  and  89  days  respectively;  litters  36-37, 
89  days;  litter  38,  79  days;  litters  56-60,  91-103  days. 

C.     Discussion  of  the  physiological  tests. 

Thyreoglobulin.  Series  I  shows  that  thyreoglobulin  possesses 
the  full  activity  per  unit  of  iodine  when  compared  with  the  dried 
thyroid  from  which  it  was  prepared.  This  is  also  confirmed  by 
series  IV  where  a  decomposition  product  obtained  from  the 
globulin  still  shows  the  complete  activity  per  unit  of  iodine. 
The  whole  of  the  physiological  activity  of  the  gland  is  therefore 
quantitatively  in  the  thyreoglobulin. 

Metaprotein.  As  stated  above,  this  still  shows  the  full  activity 
per  unit  of  iodine  although  the  percentage  concentration  of  iodine 
has  increased  from  0.465  per  cent  in  the  thyreoglobulin  to  1.52  per 
cent  in  the  metaprotein. 

lodothyrin.  None  of  the  iodothyrin  preparations  tested  was 
found  to  bring  about  a  resistance  to  acetonitrile  more  than  three- 
fourths  of  that  produced  by  the  thyroid-tissue  fed  mice.  The  indi- 
cations are  that  these  preparations  are  all  about  equally  inactive, 
lodothyrin  is  therefore  less  active  per  unit  of  iodine  than  the  thyreo- 
globulin. See  series  III  and  V. 

Primary  albumose.  This  is  still  very  active,  as  shown  by  series 
IV  and  VII;  although  the  full  activity  per  unit  of  iodine  is  not 


io8        The  Iodine  Complex  of  Thyreoglobulin 

shown  to  be  present  in  every  case  tested.  In  this  connection  it 
may  be  mentioned  that  the  results  in  series  VI  are  of  no  value. 
This  series  VI,  however  is  an  illustration  of  irregular  results,  due 
in  all  probability  to  impure  acetonitrile.  The  acetonitrile  was 
taken  from  a  freshly  opened  bottle  and  found  to  smell  decidedly 
of  hydrocyanic  acid.  Before  using,  it  was  shaken  twice  with 
saturated  potassium  carbonate  solution,  dehydrated  with  P2O6 
and  twice  distilled  from  fresh  P205.  Finally  it  was  redistilled  and 
the  fraction  collected  between  79  and  83°C.  This  distillate  was 
used  in  series  VI.  For  the  later  series  this  distillate  was  again 
purified  in  the  same  way  three  times  and  finally  redistilled  twice 
without  the  addition  of  P2O6.  Here  the  distillate  was  collected 
between  80.5  and  81.5°C. 

Secondary  albumose.  This  is  much  less  active  per  unit  of  iodine 
than  either  the  iodothyrin  preparations  or  the  primary  proteoses. 
Series  VII  shows  this,  where  the  maximum  dose  resisted  is  only 
40  per  cent  of  the  maximum  dose  resisted  by  the  thyroid-tissue 
fed  mice. 

Ammo-acids  from  the  phosphotungstic  acid  precipitate  and  the 
phosphotungstic  acid  filtrate  respectively.  The  results  in  series  IX 
indicate  that  the  former  possess  very  little  physiological  activity 
as  measured  by  the  Hunt  method.  On  the  whole,  however,  the 
results  here  are  very  unsatisfactory  as  the  mice  did  not  eat  the 
amino-acid  mixtures  well,  there  being  two  or  more  days'  feeding 
left.  The  results  indicate  that  these  amino-acid  fractions  contain 
very  little  thyroid  activity.  This  is  better  shown  in  series  X 
where  only  one-tenth  the  quantity  of  iodine-containing  substances 
was  fed.  Although  the  mice  fed  with  dried  thyroid  tissue  resisted 
an  amount  over  two  and  a  half  times  that  of  the  control  mice,  still 
the  mice  fed  with  the  same  amount  of  iodine,  but  in  the  form  of 
amino-acids,  resisted  very  little,  if  any,  more  of  the  acetonitrile 
than  the  control  mice.  In  other  words,  these  amino-acid  fractions 
show  a  very  slight  physiological  activity,  if  indeed  they  possess 
any  activity  whatever. 

Tetra-iodohistidine  anhydride  and  iodotryptophane.  These  sub- 
stances when  fed  in  amounts  representing  ten  times  the  amount 
of  iodine  fed  as  thyroid  tissue  do  not  appreciably  increase  the 
resistance  to  acetonitrile.  See  series  II  and  VIII. 


Fred  C.  Koch 


109 


Table  II  gives  a  summary  of  the  results  above.  The  relative 
physiological  activity  is  expressed  (on  the  basis  of  feeding  the  same 
amount  of  iodine  in  each  case)  as  follows :  representing  in  each  case, 
by  100,  the  largest  dose  of  acetonitrile  from  which  the  thyroid- 
tissue  fed  mice  recovered,  then  the  other  figures  represent  the 
proportions  the  limiting  doses  of  the  otherwise  fed  mice  bear  thereto. 

TABLE  II. 


RELATIVE 
ACTIVITY 

IODINE  IN  THE 
SUBSTANCE 

TOTAL  IODINE 
IN  THB  TISSUE 

Thyroid  tissue  
Thyreoglobulin                                .    . 

100 
100 

•per  cent 

0.247 
0  465 

per  cent 

100.0 
100  0 

Metaprotein 

100 

1  520 

12    0 

lodothyrin  

50-75 

4  46-7  51 

18  3 

Primary  albumose  .    . 

80-100 

0  220 

3  *> 

Secondary  albumose 

40 

0  0695 

i    z 

Amino-acids  precipitated  by  phos- 
photungstic  acid  
Amino-acids   not   precipitated  by 
phosphotungstic  acid  

0(+?) 
0(+?) 

0.0043 
0  0044 

Tetra-iodohistidine  anhydride  
lodotryptophane 

0 

o 

65.00 
41  70 

These  results  show  that  both  the  thyroid  activity  and  iodine 
may  be  concentrated  from  thyroid  tissue  in  the  thyreoglobulin 
as  well  as  in  the  metaprotein  and  iodothyrin  from  the  latter.  Per 
unit  of  iodine,  however,  we  have  full  activity  retained  in  the  thyreo- 
globulin and  metaprotein  only.  In  the  primary  albumose  frac- 
tion we  have  a  lowering  in  the  percentage  concentration  of  iodine 
and  also  a  slight  lowering  in  the  physiological  activity  per  unit 
of  iodine.  In  the  secondary  albumose  this  is  still  more  marked. 
In  the  amino-acid  fractions  the  activity  is  extremely  low  if  present. 
In  view  of  the  researches  of  Hunt  and  Seidell  with  various  iodine 
compounds  and  in  view  of  the  results  obtained  here,  we  cannot 
attribute  the  protective  action  in  any  of  these  cases  to  iodine  itself, 
but  to  a  specific  iodine-containing  complex  in  the  thyreoglobulin. 
It  is  significant  to  note  that  the  highest  physiological  activity  per 
unit  of  iodine  is  found  in  the  original  protein  and  in  the  more  com- 
plex products  of  hydrolysis.  Since  the  lowest  products  of  hydroly- 
sis are  still  less  active  per  unit  of  iodine  than  the  secondary  albu- 


f 


no        The  Iodine  Complex  of  Thyreoglobulin 

mose  it  indicates  either  that  the  iodine  group  is  altered  in  the 
hydrolysis,  or  that  the  iodine-containing  group  when  in  simpler 
combination  or  when  separated,  does  not  possess  the  full  specific 
thyroid  activity.  That  the  iodine-containing  group  when  once 
separated  would  not  possess  the  full  activity  is  not  at  all  unlikely, 
but  we  would  be  inclined  to  expect  it  to  show  some  activity; 
at  least  when  given  in  amounts  such  as  were  employed  by  Strouse 
and  Voegtlin  with  iodotyrosine  and  by  the  author  in  the  experi- 
ments with  tetra-iodohistidine  anhydride  and  iodotryptophane. 
The  indications  as  to  the  presence  of  tyrosine  and  tryptophane  in 
iodothyrin  are  very  favorable,  both  from  the  chemical  studies  on 
iodothyrin  and  also  from  similar  studies  on  iodine-free  melanoi- 
dins.24  It  is  not  likely  that  the  iodine  is  split  off  and  then  later 
added  to  the  melanoidin  fraction;  it  is  more  likely  that  it  is  already 
present  in  the  globulin  in  the  melanoidin-forming  groups  and  re- 
mains in  the  original  position  in  these  groups,  but  that  the  groups 
themselves  are  changed  in  regard  to  each  other  and  thus  the  activ- 
ity affected  to  some  extent;  a  poly-iodo  derivative  may  be  changed 
to  a  mono-iodo  derivative  and  then  may  show  decided  differences 
in  physiological  activities.  If  this  were  not  the  case  we  would 
expect  artificially  iodized  melanoidins  to  show  a  decided  thyroid 
activity.  Furthermore,  it  is  not  likely  that  sufficient  hydriodic 
acid  is  split  off  in  the  early  stages  of  the  hydrolysis  to  yield  as  much 
iodine  as  is  contained  in  the  melanoidin  fraction.  Finally,  it  is 
not  at  all  improbable  that  we  here  have  to  do  with  a  specific 
iodophore  group  just  as  in  hemoglobin  we  have  the  chromophore 
group  containing  the  iron.  The  negative  results  with  artificially 
iodized  proteins  speak  strongly  in  favor  of  this  view. 

CONCLUSIONS. 

1.  The  full  activity  of  thyroid  tissue  is  contained  in  the  thyreo- 
globulin  fraction  when  this  activity  is  measured  by  the  Hunt 
method. 

2.  The  full  activity  per  iodine  unit  is  still  present  in  the  meta- 
protein  fraction  from  this  globulin,  although  the  iodine  content 
in  the  metaprotein  fraction  has  been  increased  over  threefold  that 
of  the  globulin  itself. 

24  Samuely:  Hofmeister's  Beitr.age,  ii,  p.  355,  1902. 


Fred  C.  Koch  in 

3.  The  other  products  of  the  hydrolysis  studied,  primary  albu- 
mose,  iodothyrin  and  secondary  albumose,  show  a  gradual  decrease 
in  activity  per  unit  of  iodine  in  the  order  given. 

4.  The  amino-acid  fractions  precipitated  and  not  precipitated 
by  phosphotungstic  acid  from  the  partially  hydrolyzed  thyreo- 
globulin  still  contain  very  small  amounts  of  iodine  and  per  unit 
of  iodine  are  either  extremely  low  in  activity  or  entirely  inactive. 

5.  Tetra-iodohistidine  anhydride  and  iodotryptophane  do  not 
possess  thyroid  activity  as  determined  by  the  Hunt  method. 

I  wish  to  express  my  thanks  to  Prof.  A.  P.  Mathews  for  sug- 
gestions made  in  the  course  of  the  work. 


H2         The  Iodine  Complex  of  Thyreoglobulin 

SERIES  I.     February  25-March  8. 


MOUSE 

(")cf  
(6)  9  

LITTER  NO. 

4 
4 
4 
4 

FED  DAILY  WITH  CRACKER 
DUST  PLUS 

FATAL 
DOSE  OK 
ACETO- 
NITRILE 

DEATH 
OCCURRED 
AFTER 

DOSE  OF 
ACETO- 
MTHILE 
FROM 
WHICH 
RECOVERY 
OCCURRED 

mg.  per  gm. 

0.4 

Gravid, 
Escaped 

krg. 

n 

not  injec 
from  cag 

mg.  per  gm. 

0.35 
ted 

g 

3  79 
3.50 

(c)  9 

(d)  9  

0)  9 

4 
3 
3 

!1  mg.  dried  hog  thy- 
roid  (=0.00247 
mg.  I) 

4.49 
died  whi 
4.0 

3* 

le   feedin 
30 

(/)  cf 

(a)  cf  .. 

(h)  9  . 

3 
3 
3 

j  0.531    mg.     thyreo- 
f      globulin 
J       (  =0.00247  mg.  I) 

4.0 

U 

(i)  9  
(7)  9 

SERIES  II.    April  Si-May  1. 


(a)  cf  

3 

0  55 

41 

5 

4 

(c)j  (Ser.I)... 

3 

0 

(rf)i  (Ser.I).. 

3 

0 

(e)  cf 

2 

)1  mg.  dried  hog  thy- 

5.0 

31 

(/)  cf  

2 

roid  (=0.00247 

4.0 

4 

(o)  cf 

2 

mg  I) 

4  ^ 

00 

(/O  9  

4 

0  00392   mg    tetra- 

(i)  9  

4 

iodohistidine    an- 

0.60 

<H 

(j)  9  . 

4 

hvdridp 

n   rr 

01 

(  =0.00247  mg.  I) 

02 

.        > 

(fc)  cf  

3 

10.0392    mg.     tetra-l      0.55 

5 

(09  

4 

iodohistidine  an- 

3.55 

48 

(m)  b  (Ser.I). 

4 

hydride 

0 

(  =0.0247  mg.  I) 

SERIES  III.    May  19-29. 

(a)<?... 

6-10 
6-10 
9 
9 

0.30 

died  whi 
0.50 

5f 

le   feedin 

o 

0.45 
g 

(b)  9 

(c)  cf  
(d)  cf  

*  Slight  loss  In  injection, 
t  Not  well  when  injected. 

Fred  C.  Koch 

SERIES  III — Continued. 


MOUSE 

LITTER  NO. 

FED  DAILY  WITH  CRACKER 
DUST  PLUS 

FATAL 

DOSE  OF 
ACETO- 
NITRILE 

DEATH 
OCCURRED 
AFTER 

DOSE  OF 
ACETO- 
NITRILE 
FROM 
WHICH 
RECOVERT 
OCCURRED 

(e)  <?  v  .  .  . 

9 
6-10 
6-10 

)1  nag.  dried  hog  thy- 
roid (  =  0.00247 
mg.  I) 

mg.  per  gm. 

3.5 
3.2 

hrs. 

7 
30 

mg.  pergm. 
2.9 

(/)  9  
(0)d<  

(h)  d*  

9 
6-10 
6-10 

10.0424  mg.  iodothy- 
rin  (a)  (  =  0.00247 
mg.  I) 

2.0 
3.0 

8 
2 

1.5 

(i)  9 

(j)<?  

(k)  <? 

9 
6-10 
6-10 

0.0329  mg.  iodothy- 
rin  (6)  (=0.00247 
mg.  I) 

<2.5 
died  whi 
died  whi 

2 
le  feedin 
le  feedin 

g 
g 

(Z)  9     

Cm)  d" 

(n)  9  
(o)  9  
(p)  9  

6-10 
6-10 
6-10 

1  0.0554  mg.  iodothy- 
|      rin  (c)   (=0.00247 
J       mg.  I) 

died  whi 
2.5 

le  feedin 

8 

g 

1.5 

SERIES  IV.     June  19-29. 


(a)cf  

(6)  9 

11-12 
11-12 
11-12 

1  mg.  dried  hog  thy- 
roids (=0.00247 

rr>rr      "H 

3.0                3 

i 
died  whi  le   feedin 

2.5 
g 

(c)  <?  

(d)  9  

11-12 

mg.  JJ 

2.0 

(e)<?  

11-12 

10.163  mg.  metapro- 

2.0 

(/)9  

11-12 

tein  (A4) 

2.5 

(<7)  9  

11-12 

(=0.00247  mg.  I) 

3.0 

3 

(ft)  9  

11-12 

1  .  123  mg.   primary 

2.5 

(0  9  

11-12 

albumose  (As) 

died  whi 

le  feedin 

g 

(=  0.00247  mg.  I) 

SERIES  V.     August  2-12. 


(6)  c? 

13-14 
13-14 

)1  mg.  dried  hog  thy- 
roid (=0.00247 

died  whi 

(c)  9.  

13-14 

mg.  I) 

(d)  9  
(e)  <?  

m  9.. 

13-14 
13-14 
13-14 

1  0.0424  mg.  iodothy- 
[      rin  (a)  (  =  0.00247 
me.  I) 

died  whi 

feedin  g 


3 
feedin  g 


2.0 


1  Slight  loss  in  injection. 


H4         The  Iodine  Complex  of  Thyreoglobulin 


SERIES  V — Continued. 


• 

!      DOSE  OF 

ACETO- 

MOUSE 

LITTER  NO. 

FED  DAILY  WITH  CRACKER 
DUST  PLUS 

DOSE  OF 
ACETO- 

DEATH 
OCCURRED 
AFTER 

NITRILE 
FROM 
WHICH 

NITRILE 

1  RECOVERY 

OCCURRED 

mg.  per  gm. 

hrs. 

mg.  per  gm. 

(g)  9  .  . 

13-14 

{0.0556  mg.  iodothy- 

died  whi 

le   feedii* 

g 

(A)  9  

13-14 

rin  (c)  (=0.00247 

2.5 

3| 

mg.I) 

SERIES  VI.     November  24-December  4- 


(a)  9  
(6)  c?  

29-30 
29-30 
29730 

I  1  mg.  dried  hog  thy- 
[      roids  (=0.00247 
j       mg.  I) 

2.5 
3.0 
2.0 

<24 

1| 

<18 

(c)cf  

(d)  <?  
(e)  9  
(/)  cT  

29-30 
28 
29-30 

11  .  123  mg.   primary 
albumose  (A5) 
(=  0.00247  mg.  I) 

died  whi 
2.0 

le   feedin 
36-40 

(fl)<f.. 

28 
28 
28 

13.55  mg.  secondary 
albumose  (Ae) 
(=0.00247  mg.I) 

1.5 
2.0 
1.25 

<  4 

24-36 
20-36 

(A)  9   .. 

(i)c?  

2.5 


SERIES  VII.    January  13-23. 


(a)  9  

(&)rf  
(c)  9  .... 

31-34 
31-34 
31-34 
31-34 

1  mg.  dried  hog  thy- 
>      roid  (  =  0.00247 
j      mg.  I) 

died  whi 

le   feedin 

• 

2.0 
2.5 
3.0 

Wcf  :. 

(e)  cf  

31-34 
31-34 
31-34 
31-34 

11.123  mg.    primary 
albumose  (As) 
(=0.00247  mg.I) 

2.8 
3.0 

>  6 
>  8 

2.5 
2.0 

(/)  9  

(g}  9  .  . 

(h)  9  .... 

(»)cf  

0')<?  

(A:)  9..'.  
(0  9 

31-34 
31-34 
31-34 
31-34 

(3.55  mg.  secondary 
albumose  (A«) 
(=0.00247  mg.I) 

2.0 
1.2 
1.0 

V 

>  4 

24 

1.2 

Fred  C.  Koch 


SERIES  VIII.     February  17-27. 


MOUSE 

LITTER  NO. 

FED  DAILY  WITH  CRACKER 
DUST  PLUS 

FATAL 
DOSE  OF 
ACETO- 
NITRILE 

DEATH 
OCCURRED 
AFTER 

DOSE  OF 
ACETO- 
NITRILE 
FROM 
WHICH 
RECOVERY 
OCCURRED 

(a)  9 

33-35 

mg.  per  gm. 

hrs. 

mg.  per  gm. 

0.45 

(6)  9  
(c}  9  
(d)  9  . 

33-35 
33-35 
33-35 

0  55 

<18 

0.40 
0.35 

(e)  &  

33-35 

4.0 

2 

(/)c7  
(a)  9  .  . 

36-37 
36-37 

1  mg.  dried  hog  thy- 
roids (=0.00247 

died  whi 
3.0 

le   feedin 
6 

g 

(/O  9  

36-37 

mg.  I) 

2.0 

(o  cf  ;  .  . 

O')cf  
(k)  9    .     . 

33-35 
33-35 
36-37 

10.0059  mg.  iodotryp- 
tophane 

0.55 
1.6 
1  0 

>36 
2* 

18 

(09  

36-37 

(  =  0.00247  mg.  I) 

0.45 

>24 

(TO)  cf  

33-35 

)  0.059  mg.  iodotryp- 

10 

<  3 

(n)cf  
(o)  9    

33-35 
33-35 

tophane 
(  =0.0247  mg.  I) 

0  70 

<18 

0.5 

SERIES  IX.     March  12-22. 


(a)  a  Ser.  VIII 
(6)  6  Ser.  VIII 
(c)  c  Ser.  VIII 
(d)n  Ser.  VIII 

33-35 
33-35 
33-35 
33-35 

11  mg.  dried  hog  thy- 
roid (  =  0.00247 
mg.I) 

4.0 

did  not 

<  6 

eat;  not 

3.5 
injected 
3.0 

(«)  9  
(/)  9  

38 
38 
38 

]  33.6    mg.    P.  T.  A. 
[      Ppt.  1  (=0.00247 
j      mg.  I) 

died  whi 
died  whi 

le  feedin 
le   feedin 

g 

g 
0.8* 

(fc)cf  

(l)  cf  

38 

38 

38 

]  lOOmg.  P.T.A.  Filt. 
[      1    (=0.0024  mg. 
J      D 

1.0 

0.8 
0.6 

<  3* 

<18* 
<18* 

• 

*  Two  or  more  days  feeding  left.  This  experiment  is  not  reliable  as  animals  were  used  which 
had  recovered  in  previous  experiments  and  the  differences  in  age  were  too  great  for  such  young 
animals. 


n6        The  Iodine  Complex  of  Thyreoglobulin 


SERIES  X. 


MOUSE 

LITTER  NO. 

FED  DAILY  WITH  CRACKER 
DUST  PLUS 

FATAL, 
DOSE  OP 
ACETO- 
NITRILE 

DEATH 
OCCURRED 
AFTER 

DOSE  OF 
ACETO- 
NITRILB 
FROM 
WHICH 
RECOVERY 
OCCURRED 

(a)rf  

(6)  d*  

56-60  ' 
56-60 
56-60 
56-60 

mg.  per  gm. 

0.5 
died  whi 

hrs. 

<10 
e   feedin 

mg.  per  gm. 

g 
0.4 

0.35 

(c)  9  

(d}<?  

(e)  cf  

56-60 
56-60 
56-60 
56-60 

0.1    mg.    dried   hog 
>      thyroid 
(=  0.000247  mg.  I) 

1.2 
not  injec 

3* 

ted,  grav 

1.1 
1.0 
id 

(/)  cf  . 

(0)  9  •  • 

(A)  9  

(i)  d1  .  .  .  . 

56-60 
56-60 
56-60 
56-60 

1  5.74    mg.     P.  T.  A. 
>      Ppt.  2  (=0.000247 

j       mg.  I) 

0.5 
1.0 

0.8 

48* 
<  6f 
<16 

0.4 

C/)c?  
(fc)rf1  

(/)9  

(w)cf  

(n)  d\ 

56-60 
56-60 
56-60 
56-60 

, 

15.61    mg.     P.  T.  A. 
Filt.  2  (=0.009247 
mg.  I) 

1.0 

0.8 
0.7 

3| 
<12 
24 

0.5 

(o)  d"  

(p)  d*.... 

*  Two  days'  feeding  left. 

t  About  one  day's  feeding  left. 


Reprinted  from  THE  JOURNAL  OF  BIOLOGICAL  CHEMISTRY,  VOL.  XIV,  No.  3,  1913. 


CONTRIBUTIONS   TO    THE  CHEMICAL    DIFFERENTIA- 
TION OF  THE  CENTRAL  NERVOUS  SYSTEM. 

I.  A  COMPARISON  OF  THE  BRAIN  OF  THE  ALBINO  RAT  AT  BIRTH 
WITH  THAT  OF  THE  FETAL  PIG. 

BY  MATHILDE  L.  KOCH. 

(From  the  Hull  Laboratory  of  Biochemistry  and  Pharmacology,  University  of 
Chicago,  and  the  Wistar  Institute  of  Anatomy,  Philadelphia.) 

(Received  for  publication,  February  20, 1913.) 
INTRODUCTION. 

For  the  study  of  the  progressive  changes  in  the  central  nervous 
system  during  growth  and  senescence,  the  albino  rat,  on  account 
of  its  small  size,  short  span  of  life  and  its  powers  of  rapid  reproduc- 
tion1 is  especially  suited.  Its  growth  processes  are,  moreover, 
strikingly  like  those  of  man,  as  has  been  brought  out  by  the  exten- 
sive investigations  of  Dr.  Donaldson  within  the  past  few  years. 
It  was,  therefore,  decided  to  use  this  animal  for  a  study  of  the 
chemical  differentiation  of  the  central  nervous  system  during 
growth. 

The  youngest  brains  which  could  be  conveniently  collected  for 
chemical  analysis  were  those  of  rats  just  born.  As  it  was  not 
certain  that  the  rat  at  this  period  of  development  was  sufficiently 
immature  (chemically  undifferentiated)  to  serve  as  the  starting 
point  for  such  a  growth  series,  it  was  suggested  by  my  brother, 
Dr.  Waldemar  Koch,  that  the  brain  of  the  new  born  rat  be  com- 
pared chemically  with  the  brain  of  the  fetal  pig,  collected  at  vari- 
ous stages  of  fetal  life. 

By  such  a  comparison  we  hoped  to  determine  the  physiological 
age  of  the  rat  at  birth  in  terms  of  fetal  pig  material;  and  to  obtain, 
possibly,  from  the  pig  fetus,  material  which  would  be  more  imma- 
ture than  the  new  born  rat. 

1  H.  H.  Donaldson:  President's  Address,  Journ.  of  Nervous  and  Mental 
Disease,  xxxviii,  p.  258,  1911. 

267 


268          Chemical  Differentiation  of  the  Brain 

MATERIAL   AND    METHODS. 

The  rat  material  was  obtained  from  the  Wistar  Institute  of 
Anatomy,  which  supplied  the  brains  of  rats  of  known  age,  from 
animals  which  had  been  raised  under  constant  conditions;  two 
factors  which  are  absolutely  essential  for  such  a  study.  The 
material  was  collected  by  Dr.  Hatai  and  the  method  used  was  that 
adopted  by  the  Institute.  This  in  brief  is  as  follows :  the  rat  was 
chloroformed;  the  skull  opened  from  the  dorsal  side;  the  division 
between  the  brain  and  the  cord  made  at  the  tip  of  calamus  scrip- 
torius;  and  the  brain  removed.  The  meninges  of  the  brain  were 
left  intact.  Such  blood  as  it  contained  was,  therefore,  included 
in  the  weight.  Immediately  after  removal  the  brain  was  placed 
in  a  closed  weighing  bottle,  quickly  weighed  to  within  10  mgms.2 
and  transferred  to  a  wide  mouthed  bottle  of  300  cc.  capacity  con- 
taining absolute  alcohol.  The  weighing  bottle  was  weighed  back 
and  the  difference  recorded  as  the  weight  of  the  sample.  As  the 
weight  of  one  brain  from  rats  at  this  early  age  is  0.2  —  0.3  gram 
and  as  it  takes  at  least  from  25  to  50  grams  to  make  one  sample 
for  analysis,  a  large  number  of  brains  had  to  be  collected  (100 
brains  of  the  rat  at  birth  for  one  25-gram  sample).  As  this  cov- 
ered a  period  of  several  weeks  it  was  necessary  to  heat  the  sample 
from  time  to  time  in  a  water  bath  kept  at  a  temperature  of  70°C. 
to  insure  a  thorough  penetration  of  the  alcohol  and  sterilization. 
The  amount  of  alcohol  was  so  adjusted  as  to  make  the  final  concen- 
tration not  less  than  80-85  per  cent.  A  well  fitting  cork  stopper 
covered  with  tin-foil  was  now  inserted  and  the  bottle  carefully 
shaken  to  insure  a  uniform  mixture.  The  dates  of  collection  of  the 
samples  were  recorded,  as  the  time  a  sample  has  been  kept  in  some 
cases  influences  the  analytical  results.3  The  tightly  corked  bottles 
were  then  shipped  to  the  Laboratory  of  Biochemistry  of  the  Uni- 
versity of  Chicago,  where  the  samples  were  analyzed  according  to 
Koch's  methods  of  tissue  analysis.4 


2  A  coarse  weighing  of  the  brain  was  permissible  in  this  instance  as  it  was 
not  the  exact  brain  weight  that  was  sought  but  merely  data  for  indicating 
roughly  when  the  required  amount  of  material  had  been  obtained. 

3  W.  Koch:  Methods  for  the  Quantitative  Chemical  Analysis  of  Animal 
Tissue,  Journ.  of  the  Amer.  Chem.  Soc.,  xxxi,  p.  1340,  1909. 

4  Ibid.,  pp.  1329-64. 


Mathilde  L.  Koch  269 

The  fetal  pig  material  was  collected  by  my  brother  at  the  Chicago 
Stock  Yards.  The  fetuses  selected  were  50,  100,  and  200  mm.  in 
length.  The  pregnant  uterus  was  opened :  and  the  fetuses  removed. 
The  neck-rump  length  of  each  litter  was  taken  and  if  the  average 
length  corresponded  to  one  of  the  three  sizes  mentioned  above, 
the  entire  litter  was  taken,  placed  upon  ice  and  in  this  chilled 
condition  taken  to  the  laboratory,  where  the  brains  were  immedi- 
ately removed,  preserved  and  later  analyzed  according  to  the 
same  methods  used  for  the  rat  material. 

RESULTS   OF  ANALYSES. 

The  results  from  the  chemical  analysis  of  the  brains  from  the 
new  born  rat  and  the  adult  rat  are  given  in  table  I:  those  of  the 
50,  100,  and  200  mm.  pig  fetuses  are  recorded  in  table  II,  and 
table  III  gives  the  summary  of  all  the  averages  which  have  been 
taken  from  the  figures  which  were  most  consistent.  The  brain  of 
the  200  mm.  pig  fetus  was  plainly  more  differentiated,  it  is  there- 
fore left  out  of  table  III  and  of  the  final  discussion  of  results. 

DISCUSSION   OF   CHEMICAL   RESULTS. 

Before  taking  up  a  comparison  of  the  new  born  rat  with  the 
pig  fetus  it  may  be  well  to  state,  briefly,  the  chief  chemical  changes 
in  nervous  tissue  during  growth.  It  is  well  known  that  the  chemi- 
cal composition  of  a  tissue  varies  with  age  and  that  the  water 
content  is  one  of  the  most  important  variables.  Donaldson  states 
that,  "the  progressive  diminution  of  the  percentage  of  water  in 
the  brain  is  a  function  of  age  and  is  not  significantly  modified  by 
any  conditions  to  which  the  animals  have  been  thus  far  experi- 
mentally subjected."5  He  suggested  that  this  "is  to  be  regarded 
as  an  index  of  fundamental  chemical  processes,  which  take  place 
in  the  more  stable  constituents  of  the  nerve  cells."6  The  principal 
chemical  differences  due  to  growth,  noted  by  my  brother,  are,  "a 
decrease  in  moisture,- proteins,  extractives,  and  ash  as  the  brain 
increases  with  age,  and  an  increase  in  cerebrosides,  sulphatides, 

5  H.  H.  Donaldson :  On  the  percentage  of  Water  in  the  Brain  and  in  the 
Spinal  Cord  of  the  Albino  Rat,  Journ.  of  N enrol,  and  Psychol.,  xx,  p.  143, 
1910. 

6  Ibid. 


270 


Chemical  Differentiation  of  the  Brain 


phosphatides,  and  cholesterol;  in  other  words,  an  increase  in  sub- 
stances which  predominate  in  the  fibres  (medullated  sheath) 
during  growth."7  These  same  differences  are  to  be  found  in  all 

TABLE  I. 

Relative  proportion  of  the  proximate  constituents  of  the  brain  of  the  albino  rat 
at  birth  and  when  adult. 


ALBINO  RAT 
(AT  BIRTH) 

ALBINO  RAT 

(ADULT) 

Moist  weight  of  or 
Solids  in  per  cent. 

le  brain 

0.25 
10.42 

0.25 
10.42 

1.667 
21.9 

Dry  weight  of  one 
Number  of  brains 

brain  :  .  .  . 
in  sample  

0.026 

.    • 

100 

0.026 
100 

0.380 
31 

In  relative  proportions  of  solids. 


Proteins                            

57.16 
14.8 
0.0* 
1.5 

16.5 
(10.04) 

0.96 
1.82 

57.30 
15.6 
0.0 
1.4 

19.3 

(6.4) 

1.04 
1.92 

48.5 
22.0 
9.0 
4.6 

9.8 
(6.1) 

0.58 
1.39 

Phosphatides                                    •  •  • 

Cerebrosides  

Sulphatides                                 

Organic  extracts  1 
Inorganic  const  .  J 
Cholesterol      |  ,. 

Undetermined  J 
Total  S 

Total  P  

Distribution  of  sulphur  in  per  cent  of  total  S. 


Protein  S 

31.02 
3.2 
49.14 
16.6 

30.02 
2.8 
47.26 
19.95 

64.2 
15.6 
14.2 
6.0 

Lipoid  S  

NeutralS..  . 

Inorganic  S  

Distribution  of  phosphorus  in  per  cent  of  total  P. 

Protein  P 

13.3 
33.2 
53.5 

33.0 
53.6 

6.8 
67.6 
25.6 

Lipoid  P  

Water-soluble  P  

•Mendel,  L:  Amer.  Journ.  of  Physiol.,  xxi,  p.  104,  1908. 
t  By  difference. 

7  W.  Koch  and  S.  A.  Mann:  A  Comparison  of  the  Chemical  Composition 
of  Three  Human  Brains  at  Different  Ages,  Journ.  of  Physiol,  xxxvi, 
pp.  1-3.  (From  the  Proceedings  of  the  Physiological  Society,  November 
23,  1907). 


Mathilde  L.  Koch 


271 


TABLE  II. 


Relative  proportions  of  the  proximate  constituents  of  the  brain  of  the  fetal  pig 

at  different  ages. 


50  MM.  PIG  FETUS 

100  MM.  PIG  FETUS 

200  MM. 

PIG  FETUS 

Year  of  analysis  

'  '11 

'12 

'12 

'11 

'12 

'12 

'11 

10.1 

Moist    weight    of    one 
brain  

0.40 

8.75 

0.43 

9.87 

0.47 
9.04 

1.8 
9.1 

1.91 

8.98 

2.15 

8.98 

Solids  in  per  cent  

Dry  weight  of  one  brain 

0.035 

0.042 

0.042 

0.164 

0.171 

0.193 

Number    of    brains    in 
sample 

65 

111 

109 

35 

27 

27 

In  relative  proportions  of  solids. 


Proteins  

56.6 
13.0 

2.4? 
22.20 

2.4* 
(3.4) 

0.67 
1.74 

58.2 
15.04 

0.8 
20.5 

2.4* 
(3.06) 

0.59 

1.85 

54.61 
15.79 

1.05 
23.84 

2.4* 
(2.31) 

0.58 
1.90 

51.5 
15.7 

1.8? 
24.2 

4.4* 
(2.4) 

0.59 
1.76 

51.81 
16.31 

0.96 
24.92 

4.4* 
(1.6) 

0.57 
1.91 

52.34 
14.85 

0.84 
25.44 

4.4* 
(2.13) 

0.55 
1.82 

43.8 
17.2 

0.00? 
23.2 

(8.42) 

0.55 
1.45 

Phosphatides  

Cerebrosides 

Sulphatides  

Organic  extract    1 
Inorganic  const.  / 
Cholesterol  
Undetermined  f 

TotalS  

Total  P 

Distribution  of  sulphur  in  per  cent  of  total  S. 

ProteinS  
Lipoid  S  
Neutral  S 

54.3 
7.2? 
29.3 
9.0 

57.3 
2.67 
29.4 
10.67 

55.8 
3.59 
27.6 
13.0? 

58.4 
6.1? 
26.7 
9.0 

57.8 
3.36 
28.97 
9.93 

55.66 
2.98 
31.68 
9.6 

60.9 
0.00? 
25.5 
13.33 

Inorganic  S 

Distribution  of  phosphorus  in  per  cent  of  total  P. 

Protein  P  
Lipoid  P  

1 
31.6 
53.6 

15.7 
32.4 
51.8 

14.0 
29.6 
56.2 

35.5 

14.5 
34.5 
50.9 

14.6 
31.6 
53.8 

5.2 
46.3 
48.5 

Water-soluble        .   .  . 

*  Mendel,  L.:  Amer.  Journ.  of  Physiol.,  xxi,  p.  103,  1908. 

t  By  difference. 

(?)  Indicates  doubtful  result. 

THE  JOURNAL  OF  BIOLOGICAL  CHEMISTRY,    VOL.   XIV,   NO.  3. 


272  Chemical  Differentiation  of  the  Brain 


TABLE  III. 


Relative  proportions  of  the  proximate  constituents  of  the  brain  of  the  fetal  pig 
at  different  ages  compared  with  the  brain  of  the  albino  rat  at  birth.  (Aver- 
ages of  the  foregoing  determinations.} 


PIG  FETUS 

ALBINO  RAT 

50  mm. 

100  mm. 

at  birth 

adult 

Moist  weight  of  one  brain  

0.433 
9.22 

0.039 
95 

1.90 

8.99 
0.171 
30 

0.25 

10.42 
0.026 
100 

1.667 
21.9 

0.380 
31 

Solids  in  per  cent                   

Dry  weight  of  one  brain 

Number  of  brains  in  sample  

In  relative  proportions  of  solids. 


Proteins                                           .    . 

56  47 

51  88 

57  23 

48  5 

Phosphatides  

15.41 

15.62 

15.2 

22.0 

Cerebrosides*  .... 

0  0 

0.0 

0  0 

9.0 

Sulphatides 

0  92 

0  90 

1  45 

4  6 
*•« 

Organic  extract  1 

22  18 

24  69 

17  9 

9  8 

Inorganic  const.  / 
Cholesterol  

2.4f 

4.4t 

Undetermined!  :  
Totals  

(2.59) 
0  585 

20.49 
0  57 

(8.22) 
1  00 

(6.1) 
0  58 

Total  P.  .  . 

1  83 

1  83 

1  87 

1  39 

Distribution  of  sulphur  in  per  cent  of  total  S. 


Protein  S  

55  8 

57  28 

30  52 

64  2 

Lipoid  S  .  . 

3  13 

3  17 

3  0 

15  6 

Neutral  S  

28  7 

29  11 

48  2 

14  2 

Inorganic  S.  . 

9  83 

9  51 

18  27 

6  0 

Distribution  of  phosphorus  in  per  cent  of  total. 


Protein  P  

14.8 

14.55 

13.3 

I      6.8 

Lipoid  P.  

31.2 

33.8 

33.1 

67.6 

Water-soluble  P  

53  8 

52  3 

53  55 

25  6 

1    ^°'D 

Cerebrosides  not  determined  in  fetal  brains.    Not  present  according  to  Mendel, 
t  Mendel,  L:  Amer.  Journ.  of  Physiol.,  xxi,  p.  103,  1908. 
J  By  difference. 


Mathilda  L.  Koch  273 

nervous  tissue  during  growth  and  may  therefore  be  used  in  making 
a  comparison  between  the  brain  of  the  new  born  rat  and  that  of  the 
fetal  pig  to  determine  which  is  the  more  immature. 

We  may  now  proceed  to  consider  in  detail  the  comparison  of  the 
various  constituents8  in  the  brain  of  the  new  born  rat  and  the  pig 
fetus. 

Water.  The  per  cent  of  water  in  the  brain  of  the  new  born 
rat  is  closely  similar  to,  but  a  little  lower  than,  that  of  either  the 
50  mm.  or  100  mm.  pig  fetus.  This  would  indicate  that  the  rat  is 
of  about  the  same  physiological  age  as  these  fetuses,  since  the 
differences  are  within  the  limits  of  error. 

Protein.  The  per  cent  of  protein  in  the  total  solids  is  higher  in 
the  brain  of  the  new  born  rat  than  in  either  that  of  the  50  or  the 
100  mm.  pig  fetuses.  Since  the  per  cent  of  protein  is  highest  in 
the  youngest  material,  this  is  an  indication  that  the  rat's  brain  is 
less  mature  than  that  of  the  100  mm.  pig  fetus,  but  not  very 
different  from  the  50  mm.  fetus. 

Phosphatides.  The  per  cent  of  phosphatides  is  the  same  in  the 
new  born  rat  as  it  is  in  the  50  and  the  100  mm.  pig  fetus.  This 
would  indicate  a  close  agreement  in  physiological  age  between 
these  two.  This  is  the  lowest  phosphatide  content  yet  obtained  in 
an  analysis  of  the  brain  tissue  and  approaches  that  observed  in  the 
suprarenal,  which,  among  all  the  organs,  comes  closest  to  that  of 
nervous  tissue  in  chemical  composition. 

Cerebrosides.  These  are  absent  in  both  the  new  born  rat,  and 
in  the  pig  fetus,  as  is  to  be  expected  in  nervous  tissue  before  medul- 
lation. 

Sulphatides.  The  percentage  of  sulphatides  is  about  the  same 
in  the  new  born  rat  as  in  the  pig  fetus,  which  indicates  the  same 
age. 

Organic  extractives  and  inorganic  constituents.  These  are  some- 
what higher  in  the  pig  fetus  than  in  the  new  born  rat  and,  except  as 
this  is  associated  with  the  greater  per  cent  of  lymph  in  the  embry- 
onic material,  it  would  indicate  it  to  be  more  immature  than  the 
new  born  rat. 

8  The  nature  and  significance  of  the  constituents  will  be  discussed  in  the 
third  paper  of  this  series. 


274          Chemical  Differentiation  of  the  Brain 

Cholesterol.  The  figures  for  cholesterol  were  not  determined  by 
me,  but  were  taken  from  Mendel9  and  incorporated  here  for  the 
sake  of  completeness. 

This  leaves  undetermined  from  2  to  3  per  cent  which  is  not  more 
than  would  be  expected  in  the  errors  involved  in  making  so  many 
determinations  from  one  tissue  and  calculating  approximate  con- 
stituents from  assumed  factors. 

The  distribution  of  sulphur  in  per  cent  of  total  sulphur  is  widely 
different  in  the  two  forms,  but  as  this  is  not  correlated  with  age 
but  is  apparently  a  species  peculiarity,  the  results  are  not  out  of 
harmony  with  the  foregoing  conclusions. 

The  distribution  of  phosphorus  between  the  protein,  lipoidand 
water-soluble  phosphorus  is  closely  similar  in  the  rat  and  the 
50  and  100  mm.  pig  fetus,  showing  the  physiological  ages  to  corres- 
pond. 

The  remarkably  high  figure  for  neutral  and  inorganic  sulphur  in 
the  rat  at  birth  requires  an  explanation  but  it  is  not  possible  to 
give  this  with  the  data  so  far  at  hand. 

The  general  conclusions  from  these  figures  are,  that  from  a 
chemical  standpoint  the  brain  of  the  new  born  rat  is  about  as  imma- 
ture as  that  of  the  100  mm.  pig  fetus,  being  on  the  whole  a  little 
less  differentiated  than  the  latter. 

The  differences  between  the  brain  of  the  50  mm.  and  the  100 
mm.  pig  fetus  are  not  marked,  and  this  would  indicate  that  there  oc- 
curs between  these  ages  an  increase  in  weight  unaccompanied  by  any 
significant  change  in  chemical  composition.  This  would  corres- 
pond with  the  results  of  Mendel10  and  Raske11  who  found  that  in 
the  brains  from  these  young  fetuses  there  is  no  chemical  dis- 
tinction between  grey  and  white  matter.  Moreover  the  brain 
of  the  50  mm.  pig  fetus  is  the  youngest  which  it  is  practicable  to 
obtain  for  analysis  and  even  at  this  age  the  tissues  are  so  watery 
and  filled  with  lymph  that  some  error  is  thereby  introduced  in  the 
analysis  of  the  constituent  tissues. 

Since  the  brain  of  the  50  mm.  pig  fetus  shows  no  material  differ- 
ences from  that  of  the  100  mm.  pig  fetus  and  the  latter  is  no  more 

9  L.  B.  Mendel  and  Charles  S.  Leavenworth :  Chemical  Studies  on  Growth. 
IX.  Notes  on  the  Composition  of  Embryonic  Muscular  and  Nervous  Tissues. 
Amer.  Journ.  of  PhysioL,  xxi,  p.  103,  1908. 

10  Ibid. 

11  Raske:  Zeitschr.f.  physiol.  Chem.,  x,  p.  340,  1886. 


Mathilde  L.  Koch  275 

immature  chemically  than  that  of  the  new  born  rat,  it  appears 
that  the  new  born  rat's  brain  is  as  young  nervous  material  as  can 
conveniently  be  analyzed  at  present:  and  it  forms,  therefore, 
a  convenient  starting  point  for  the  study  of  the  chemical  differen- 
tiation of  the  central  nervous  system  during  growth. 

CHEMICAL  RESULTS  COMFIRMED  BY  PHYSIOLOGICAL  AND  ANATOMICAL 

DATA. 

It  is  astonishing  that  chemically  the  brain  of  the  new  born  rat 
should  be  as  immature  as  that  of  the  100  mm.  pig  fetus,  but, 
surprising  as  this  fact  is,  it  is  substantiated  by  a  comparison  of 
the  structure  of  the  cerebellum  of  these  two  animals  and  of  their 
behavior  at  the  time  of  birth. 

It  is  a  well-known  fact  that  the  rat  is  born  in  a  very  immature 
state,  with  its  eyes  shut,  and  when  first  born,  is  capable  only  of 
movements  involved  in  sucking,  bending  the  body  and  tail  and 
making  a  squeaking  noise.12  The  pig,  on  the  other  hand,  "is  born 
with  its  eyes  open  and  requires  no  assistance  as  a  rule  in  making  its 
start  in  life.  It  is  more  or  less  able  to  walk  around  as  soon  as 
born."13  Such  a  state  of  activity  in  the  rat  is  not  reached  until 
the  period  of  weaning  17-21  days  after  birth. 

This  difference  in  physiological  behavior  is  correlated  with  the 
relative  development  of  the  cerebellum  of  the  two  animals;  par- 
ticularly as  indicated  by  the  development  and  transformation  of 
the  outer  granular  layer  of  cells.  A  comparison  of  this  layer  in 
both  animals,  founded  on  the  observations  of  Addison14  who 
studied  the  different  layers  of  the  cerebellum  in  the  albino  rat, 
and  of  Takasu15  who  studied  these  same  layers  in  the  pig  fetus, 
brought  out  the  following  facts : 


12  Wm.  H.  F.  Addison:  The  Development  of  the  Purkinje  Cells  and  the 
Cortical  Layers  in  the  Cerebellum  of  the  Albino  Rat,  Journ.  of  Comp.N enrol., 
xxi,  p.  476,  1911. 

13  Forbes:  personal  communication. 

14  Wm.  H.  F.  Addison:  Journ.  ofComp.  Neural.,  xxi,  p.  464,  1911. 

15  K.  Takasu:  Zur  Entwicklung  der  Ganglienzellen  der  Kleinhirnrinde 
des  Schweines,  Anat.  Anz.,  xxvi,  pp.  225-32,  1905. 


276          Chemical  Differentiation  of  the  Brain 


BAT 

PIG 

First  appearance  of  cells  in 
outer  granular  layer  
Division  of  layer  into  two  zones 
inner  and  outer  

19-day  fetus 
At  birth 

50  mm.  fetus 
100  mm.  fetus 

Disappearance    of    cells    from 
inner  zone  of  layer  

21  days  after  birth 

300mm.  fetus 

The  first  appearance  of  the  cells  in  the  outer  granular  layer  of  the 
cerebellum  in  the  rat  is  in  the  19-day  fetus,  and  in  the  .pig  in  the 
50  mm.  pig  fetus.  At  this  time  the  cells  are  settled  in  a  thin  layer 
(two  rows  deep)  around  the  outer  edge  of  the  cerebellar  cortex. 
This  layer  increases  until  a  considerable  depth  is  filled  in  with 
cells  which  soon  separate  into  two  strata,  an  outer  and  an  inner; 
this  separation  takes  place  in  the  rat  at  birth,  and  in  the  pig  fetus 
when  it  is  100  mm.  in  length.  The  cells  from  the  outer  granular 
layer  now  begin  to  migrate  to  the  inner  granular  layer  and  the  dis- 
appearance of  the  cells  from  this  outer  granular  layer,  which  corres- 
ponds with  the  time  of  securing  motor  control  in  an  animal,  occurs 
in  the  rat  at  the  twenty-first  day  of  life,  and  in  the  pig  when  this 
is  from  200  to  300  mm.  in  length,  or  at  birth.  These  facts  show, 
therefore,  that  the  new  born  rat  is  as  developed  with  respect  to 
motor  activity  as  the  100  mm.  pig  fetus,  and  that  the  rat  at  wean- 
ing (17-21  days  after  birth)  and  the  pig  at  birth  are  at  correspond- 
ing physiological  ages.  The  conclusion  from  this  anatomical  com- 
parison, namely,  that  the  100  mm.  pig  fetus  and  the  rat  at  birth 
are  of  like  physiological  age,  fully  confirms,  therefore,  the  conclu- 
sion drawn  from  both  chemical  and  physiological  evidence  already 
adduced. 

We  now  ask  the  question,  how  far  this  result,  that  the  nervous 
system  of  the  new-born  rat  is  chemically  as  old  as  that  of  the 
100  mm.  pig  fetus,  agrees  with  observations  made  by  Donaldson, 
that  the  rate  of  growth  and  percentage  of  water  in  the  mammalian 
nervous  system  (represented  by  the  brains  of  man  and  the  rat) 
agree  in  the  two  forms  at  equivalent  ages,  thus  indicating  that  the 
nervous  systems  are  in  corresponding  physiological  states  at  equal 
fractions  of  the  life  cycles.16 

18  H.  H.  Donaldson:  A  Comparison  of  the  White  Rat  with  Man  in  respect 
to  the  Growth  of  the  Entire  Body,  Boas  Anniversary  Volume,  1906,  pp. 
5-26. 


Mathilde  L.  Koch  277 

It  remains  therefore  to  inquire  whether  the  chemical  and  behav- 
ior relations  between  the  rat  and  pig  which  have  just  been  pointed 
out,  occur  at  equivalent  ages  in  these  two  forms. 

Great  difficulty  was  experienced  in  finding  any  statements  con- 
cerning the  age  of  the  pig  fetuses.  The  statements  of  different 
authors  did  not  always  agree,  but  the  two  which  agreed  closest 
were  those  of  Bradley17  and  Coe.18  Bradley  compared  the  length 
of  the  embryos  with  the  time  from  coition;  Coe  estimated  the  age 
from  the  rate  of  development  of  embryos  of  other  mammals. 
While  considerable  uncertainty  thus  attaches  itself  to  these  figures19 
it  may  be  assumed  that  the  50  mm.  pig  fetus  is  about  40  days  old 
from  conception:  the  100  mm.  fetus  is  55-62  days;  and  the  200  mm. 
fetus  is  from  88-90  days  from  conception. 

We  find  in  the  rat  the  period  of  gestation  is  21  days  and  its  span 
of  life  three  years  (Donaldson),  or  a  total  age  of  1116  days; in 
the  pig  the  period  of  gestation  is  125  days  and  its  normal  span  of 
life,  as  far  as  could  be  ascertained,  is  20  years,20  or  7425  days.  The 
rat,  therefore,  lives  about  one-sixth  as  long  as  the  pig.  Assuming 
that  the  rat  at  birth  has  lived  TTTG",  or  ^V,  of  its  total  life,  the 
60-day  pig  fetus  will  have  lived  yfio,  or  TTS,  of  its  life.  It  appears 
then,  if  the  total  length  of  life  given  is  correct  for  both  animals 
and  the  numbers  used  for  the  divisors  in  each  case  are  really  com- 
parable as  they  stand,  that  we  do  not  have  corresponding  physio- 
logical conditions  of  the  brain  at  equivalent  ages,  for  these  brains 


17  O.  C.  Bradley:  On  the  Development  of  the  Hind  Brain  of  the  Pig, 
Journ.  of  Anat.  and  PhysioL,  xl,  Part  I,  p.  1. 

18  Mendel  refers  to  Professor  Coe  in  Chemical  Studies  on  Growth.     I. 
The  Inverting  Enzymes  of  the  Alimentary  Tract,  especially  in  the  Embryo, 
Amer.  Journ.  of  PhysioL,  xx,  p.  90,  1907-1908. 

19  Bradley  makes  the  statement,  that  "although  the  age  of  the  different 
embryos  is  given,  it  is  not  intended  that  it  should  signify  more  than  the 
time  which  elapsed  between  the  time  of  coition  and  the  time  when  the  mother 
was  destroyed In  embryos  taken  from  two  litters  it  not  infre- 
quently happens  that  those  which  should  be  further  advanced  in  develop- 
ment, judging  from  the  period  which  has  elapsed  since  sexual  congress  took 
place,  are  as  backward,  or  even  more  backward,  than  those  of  the  'younger* 
litter."     A  more  definite  way  to  determine  the  age  of  an  embryo  would  be, 
according  to  Mall,  by  ossification.    No  data  were  available  however  for  a 
comparison  between  the  rat  and  the  pig. 

20  Longevity,  Encyclopaedia  Britannica  (Eleventh  Edition),  xvi,  p.  975. 


278          Chemical  Differentiation  of  the  Brain 

are  found  to  be  in  corresponding  states  at  the  -&V  and  the  yiur  part 
of  the  total  life  cycles.  Had  the  relation,  in  the  form  stated  above, 
held,  these  fractions  should  have  been  identical.  It  is  only  fair 
to  add,  however,  that  in  view  of  the  absence  of  precise  information 
concerning  the  pig  and  in  view  of  the  fact  that  the  early  days  of 
gestation  are  used  for  cell  division  accompanied  by  only  slight  differ- 
entiation, too  much  stress  should  not  be  laid  on  the  relation  here 
given. 

On  the  other  hand,  instead  of  taking  the  end  of  life  as  the  fixed 
point  of 'our  calculations,  we  may  consider  the  time  when  motor 
control  is  obtained  to  indicate  closely  corresponding  states  of  the 
central  nervous  system.  In  the  rat,  motor  control  is  obtained  at 
42  days  from  conception,  and  in  the  pig  at  125  days,  that  is,  at 
birth.  If  the  law  of  corresponding  states  is  correct,  the  nervous 
system  of  these  two  animals  should  be  in  corresponding  conditions 
at  the  same  fractions,  either  J,  J,  or  J  of  these  periods.  This  is 
found  to  be  the  case,  for  the  rat  is  born  after  21  days'  gestation. 
This  would  be  just  half  way  between  the  two  fixed  points  of  concep- 
tion and  time  of  gaining  motor  control  and  this  corresponds  in  the 
pig  to  just  one-half  of  its  gestation  period  or  about  62  days,  which 
is  the  age  of  the  100  mm.  pig. 

It  was  actually  found,  both  chemically  and  anatomically,  that 
the  nervous  systems  of  these  two  animals  were  in  the  same  state 
of  development  at  these  respective  periods  and  it  appears  from  these 
observations  that  Donaldson's  law  may  hold,  if  put  in  the  form: 
the  nervous  systems  of  mammals  are  in  the  same  physiological 
state  at  equal  fractions  of  their  total  periods  of  development. 

In  conclusion  it  gives  me  great  pleasure  to  thank  Dr.  H.  H.  Don- 
aldson and  Prof.  A.  P.  Mathews  for  their  many  suggestions  in 
connection  with  this  problem  and  for  their  aid  in  getting  this  paper 
ready  for  publication.  The  problem  itself  was  suggested  to  me  by 
my  brother  and  forms  the  first  of  a  series  of  papers  which  are  to 
follow  from  time  to  time,  on  the  chemical  differentiation  of  the 
central  nervous  system,  and  on  which  he  was  engaged  at  the  time 
of  his  death.  The  work  was  carried  out  in  the  Laboratory  of  Bio- 
chemistry and  Pharmacology  of  the  University  of  Chicago  and 
was  aided  by  h  grant  from  the  Wistar  Institute  of  Anatomy  and 
Biology,  Philadelphia. 


Mathilde  L.  Koch  279 

SUMMARY. 

1.  A  quantitative  determination  of  the  constituents  of  the  brain 
of  the  albino  rat  at  birth  shows  it  to  be  chemically  as  undifferenti- 
ated  as  the  brain  of  a  50  mm.  or  100  mm.  pig  fetus. 

2.  There  is  little  difference  in  chemical  composition  between 
the  50  mm.  and  the  100  mm.  pig  fetus  brain. 

3.  Since  the  50  mm.  fetus  brain  is  the  youngest  which  can  be 
analyzed  and  this  closely  resembles  the  100  mm.  fetus,  and  this 
in  turn  is  no  more  immature  than  the  new  born  rat,  it  appears  that 
the  brain  of  the  new  born  rat  is  sufficiently  immature  to  serve  as 
a  starting  point  in  a  study  of  the  chemical  differentiation  -of  the 
brain  during  growth. 

4.  That  the  brain  of  the  new  born  rat  is  as  immature  as  the 
100  mm.  pig  embryo  is  shown,  also,  by  the  similarity  of  the  changes 
in  the  outer  layer  of  cells  of  the  cerebellar  cortex  in  both  animals 
previous  to  gaining  motor  control,  and  by  the  animal's  behavior 
at  this  period. 

5.  If  the  nervous  systems  are  assumed  to  be  in  corresponding 
states  when  motor  control  is  obtained,  and  Donaldson's  law  is 
correct,  that  the  nervous  system  is  in  the  same  state  at  correspond- 
ing physiological  ages,  then  the  brain  of  the  rat  at  birth  should 
correspond  chemically  with  the  100  mm.  pig  fetus  brain.     This  is 
found  to  be  the  case. 


Reprinted  from  THE  JOURNAL  OF  BIOLOGICAL  CHEMISTRY,  VOL.  XIV,  No.  3,  1913 


CONTRIBUTIONS  TO  THE  CHEMICAL  DIFFERENTIA- 
TION OF  THE  CENTRAL  NERVOUS  SYSTEM.. 

II.  A  COMPARISON  OF  TWO  METHODS   OF  PRESERVING  NERVE 
TISSUE  FOR  SUBSEQUENT  CHEMICAL  EXAMINATION. 

BY  W.  KOCH  AND  M.  L.  KOCH. 

(From  the  Hull  Laboratories  of  Biochemistry  and  Pharmacology,  University 
of  Chicago,  and  the  Wistar  Institute  of  Anatomy,  Philadelphia.) 

(Received  for  publication,  February  20, 1913.) 

With  valuable  biological  material  it  is  sometimes  desirable  to 
make  water  estimations  and  the  estimations  of  the  other  constitu- 
ents on  the  same  sample.  This  can  be  done  somewhat  indirectly 
if  the  method  already  described1  of  placing  the  fresh,  weighed 
tissues  immediately  in  95  per  cent  alcohol  is  used. 

To  see  whether  tissues  in  which  the  water  had  been  determined 
by  drying  could  thereafter  be  analyzed  by  the  methods  referred 
to  above  and  would  yield  the  same  proportion  of  the  various  con- 
stituents as  these  same  tissues  treated  by  the  alcohol  method,  an 
analysis  was  made  of  the  brains  and  spinal  cords  of  albino  rats 
which  had  been  dehydrated  in  these  two  ways.  The  possible 
drawbacks  of  the  heat  method  of  determining  moisture,  namely,  the 
oxidation  or  decomposition  of  part  of  the  material  and  the  evapora- 
tion of  volatile  constituents,  are  obvious,  but  we  had  no  definite 
knowledge  of  how  serious  the  errors  involved  in  the  method  might 
be  in  practice. 

To  determine  to  what  extent  these  changes  took  place  and  what 
they  were,  we  analyzed  material  which  had  been  dried  at  95°C. 
for  one  week  and  which  at  the  end  of  this  time  had  been  placed  in 
alcohol,  and  compared  it  with  similar  material  which  had  been 
placed  directly  in  alcohol.  The  results  are  given  in  the  table. 

It  may  be  seen  by  a  comparison  of  the  results  of  the  two  analyses 
in  the  table,  that  decompositions  seriously  affecting  the  analyses 
are  produced  by  heat  drying,  particularly  in  the  case  of  the  brain. 
The  differences  are  most  marked  in  the  phosphorus  compounds. 

1  Koch,  W. :  Journ.  Amer.  Chem.  Soc.,  xxxi,  pp.  1353-4,  1909. 

281 


282 


Preservation  of  Nerve  Tissue 


C  tmpirison  of  brains  and  cord*  dried  at  95°C.  with  brain*  arid  cur  da  plnccd 
directly  in  alcohol  without 


ENCEPHALON 

CORDS 

Direct  Into 
alcohol 

Dried  at 
95°C. 

Direct  Into 
alcohol 

Dried  at 
95°C. 

Laboratory  number             

W  13 

W  18 

W  9 

W  20 

In  per  cent  of  total  solids. 


Proteins 

48.5 

47.9 

32.8 

29.6 

Phosphatides  

22.0 

16.2 

25  3 

22  1 

Cerebrosides               

8.4 

(?) 

12  5 

14  4 

Sulphatides 

4  5 

4.6 

70 

6.7 

Organic  ext.        } 

9  8 

12.4 

7.6 

8  0 

Inorganic  const./ 
Undetermined  lipoids 

6  8* 

14.8* 

19  2* 

Total  S                           

0.58 

0.59 

0.45 

0  42 

Total  P 

1  39 

1  31 

1.44 

1.42 

Distribution  of  sulphur  in  per  cent  of  total  S. 


ProteinS  

63.8 

64.6 

53.7 

53.3 

Lipoid  S  

15.6 

15.6 

30.9 

32.1 

Neutral  S 

14  5 

14  0 

10.3 

9.5 

Inorganic  S  

6.1 

6.0 

5.0 

5.0 

Distribution  of  phosphorus  in  per  cent  of  total  P. 


Protein  P  

6  8 

8  1 

5  6 

5  0 

Lipoid  P 

67  6 

55  1 

77  4 

69  2 

Water  Sol.  P  

25  6 

36  8 

17.0 

25.8 

'  Obtained  by  difference. 

By  drying  there  has  been  a  destruction  of  the  phosphatides  involv- 
ing a  change  in  the  distribution  of  phosphorus  in  per  cent  of  total 
phosphorus;  that  is,  a  considerable  amount  of  lipoid  phosphorus 
is  changed  to  water-soluble  phosphorus.  There  was  no  change  in 
the  sulphur  distribution.  It  will  be  noticed  that  the  phosphatides 
of  the  cord  are  more  resistant  to  heat  than  those  of  the  brain,  a 
point  of  sufficient  interest  to  justify  repetition. 

We  conclude,  then,  that  the  determination  of  water  by  drying  at 
95°C.  cannot  safely  be  used,  if  it  is  desired  to  determine  in  the  same 
sample  the  relative  proportions  of  the  solid  constituents;  and  that 
the  indirect  method  already  described  is  far  superior  for  this  pur- 
pose. 


Reprinted  from  THE  JOURNAL  op  BIOLOGICAL  CHEMISTRY,  Vol.  XV,  No.  3,  1913 


CONTRIBUTIONS  TO  THE  CHEMICAL  DIFFERENTIATION 
OF  THE  CENTRAL  NERVOUS  SYSTEM. 

III.  THE  CHEMICAL  DIFFERENTIATION  OF  THE  BRAIN  OF  THE 
ALBINO  RAT  DURING  GROWTH. 

BY  W.  KOCH  AND  M.  L.  KOCH. 

(From  the  Hull  Laboratory  of  Biochemistry  and  Pharmacology,  University 

of  Chicago,  and  the  Wistar  Institute  of  Anatomy, 

Philadelphia.) 

(Received  for  publication,  July  1,  1913.) 


The  transformations  which  occur  in  the  brain  during  growth 
offer  a  particularly  enticing  field  for  the  study  of  chemical  differ- 
entiation, not  alone  because  of  the  very  great  interest  attaching 
to  the  solution  of  the  problem  of  the  chemical  basis  of  its  func- 
tions, but  because  its  structural  differentiation  during  growth  is 
very  marked.  On  the  one  hand  there  is  the  formation  of  a  large 
amount  of  new  material  composing  the  medullary  sheath  of  the 
nerve  fibers,  and,  on  the  other  hand,  the  appearance  of  a  quantity 
of  a  peculiar  supporting  tissue,  the  neuroglia.  The  chemical 
changes  during  growth  should,  therefore,  be  very  marked;  and 
it  is  of  interest  to  discover  how  far  our  chemical  methods  enable 
us  to  follow  such  obvious  structural  modifications. 

1  Waldemar  Koch  died  at  Chicago  February  1, 1912.  As  Associate  in  Bio- 
logical Chemistry  at  the  Wistar  Institute  of  Anatomy  and  Biology,  he  spent 
the  autumn  of  1910  and  of  1911  in  Philadelphia  working  mainly  on  matters 
connected  with  this  research.  This  paper  has  been  prepared  in  considerable 
part  from  results  of  analyses  made  by  me  under  the  direction  of  my  brother, 
and  from  a  manuscript  written  by  him.  Many  additional  analyses,  which  he 
had  planned,  have  been  made  and  incorporated  into  the  series.  The  inter- 
pretations of  the  results  have  been  left  to  a  large  extent,  in  his  words.  I 
have  been  assisted  in  its  preparation  for  publication  by  Professor  A.  P. 
Mathews  and  Dr.  H.  H.  Donaldson,  the  aid  of  both  of  whom  I  gratefully 
acknowledge.— M.  L.  KOCH. 

423 


424         Chemical  Differentiation  of  the  Brain 

The  selection  of  chemical  methods  for  such  a  study  was  largely 
guided  by  the  principle  now  coming  to  be  generally  accepted, 
namely,  that  in  living  matter  we  are  not  dealing  with  an  aggre- 
gation of  more  or  less  similar,  highly  organized  and  necessarily 
complex  molecules  (Riesenmolekul  of  Pfltiger),  but  rather,  with 
a  more  or  less  heterogeneous  substratum  in  which  dissimilar  and 
not  necessarily  highly  complex  molecules,  or  their  dissociated  par- 
ticles, are  engaged  in  a  series  of  correlated  chemical  reactions. 
The  larger  aggregates  may  be  conceived  as  either  not  taking 
part  directly  in  chemical  activity,  or  as  helping  in  the  control 
and  localization  of  the  chemical  reactions,  just  as  in  a  photo- 
graphic dry  plate,  the  presence  of  the  gelatin  makes  possible  a 
high  degree  of  localization  of  the  photo-chemical  reaction.  We 
aimed,  therefore,  to  stop  the  chemical  activities  at  definite  given 
stages  during  the  growth  period  and  then  to  observe  the  differ- 
ences which  could  be  demonstrated.  From  such  data  we  then 
drew  conclusions  as  to  the  nature  of  the  transformations  which 
had  occurred  in  the  interval. 

The  methods  of  collecting  the  material  were  devised  with  this 
end  in  view,  namely,  to  stop  all  chemical  activity  as  rapidly 
and  completely  as  possible.  The  sources  of  error  due  to  post 
mortem  changes  then  became  constant,  and  we  are  in  reality 
following  a  principle  that  has  long  been  in  use  in  histological 
studies.  For  the  preserving  agent,  alcohol  was  selected,  as  it  is 
the  least  apt  to  interfere  with  the  further  chemical  procedure, 
and,  in  fact,  treatment  with  alcohol  represents  a  step  in  the 
process. 

In  the  selection  of  the  chemical  methods  for  this  series  two 
points  were  kept  in  mind: 

1.  The  necessity  of  correlating  the  chemical  observations  with 
the  known  facts  of  structure,  to  the  interpretation  of  which  they 
should  add  a  greater  precision.  As  an  example  of  this,  there 
were  studied  the  sulphatides  (lipoid  sulphur)  which  are  intimately 
associated  in  the  nervous  system  with  the  sheaths  of  the  medul- 
lated  nerve  fibers. 

2.  The  collection  of  data,  which,  correlated  with  function, 
would  give  the  physiologist  a  better  knowledge  of  the  nature  of 
his  material  and  thus  enable  him  to  do  more  than  speculate  as 
to  the  probable  nature  of  the  processes  involved  in  the  phenomena 


W.  Koch  and  M.  L.  Koch 


425 


he  is  observing.  As  an  example  of  this,  there  was  studied 
the  ratio  between  neutral  sulphur  and  protein  sulphur,  a  ratio 
which  correlates  closely  with  the  decrease  in  metabolic  activity 
associated  with  the  growth  of  the  nervous  system  from  birth  to 
maturity. 

The  general  plan  of  the  chemical  technique  has  been  first  to 
block  out  the  material  into  larger  groups  of  substances  and  then 
carry  the  procedure  of  separation  into  greater  detail.  The  neces- 
sity of  working  with  data  which  represent  something  definite  from 
the  point  of  view  of  the  chemist,  has  also  been  kept  in  mind. 

The  following  outline  illustrates  the  extent  to  which  the  chemi- 
cal procedure  has  been  carried  up  to  the  present. 

Outline  illustrating  the  separation  of  constituents  ~by  the  method  employed, z  classified 
according  to  their  state  of  aggregation. 


ENCEPHALON  DIVIDED  BY  STATE  OP  AGGREGATION  INTO: 

COLLOIDAL  (FRACTION  1  AND  4) 

NON-COLLOIDAL  (FRACTION  2  AND  3) 

Proteins 
(Fract.  4) 

Lipoids 
(Fract.  1) 

Organic 
Extractives 
(Fract.  2  and  3) 

Inorganic 
Constituents 
(Fract.  2  and  3) 

Proximate  c  o  n  - 
stituents 

(Include  sup- 
porting 
structures) 

Phosphatides 
Cerebrosides 
Sulphatides 
(  Cholesterol 
\Undetermined 

Sodium 
Potassium 
Calcium 
Magnesium 
Chlorides 

Sulphur  c  o  m  bi  - 
nations 

Protein  S 

Lipoid  S 

Neutral  S 

Inorganic  S 
(sulphates) 

Phosphorus  com- 
binations 

Protein  P 

Lipoid  P 

Organic  e  x  - 
tractives  P 

Inorganic  P 
(phosphates) 

For  an  explanation  of  the  chemical  procedure  followed  for  this 
separation  the  following  outline  has  been  inserted. 


2  The  method  employed  for  this  separation  is  described  in  an  earlier 
paper  by  W.  Koch  and  coworkers:  Journ.  of  the  Amer.  Chem.  Soc.,  xxxi, 
pp.  1342-1361, 1909. 


426         Chemical  Differentiation  of  the  Brain 

Moist  Brain  Tissue:  Add  alcohol  and  extract  alternately  with  alcohol  and 

ether.* 


EXTRACT  (FRACTION  1  AND  2) 

RESIDUE  (FRACTION  3  AND  4) 

EVAPORATE   TO    DRYNE8S,    EMULSIFY  WITH 
WATER,  PPT.  WITH  CHClsIN  0.5 
PER  CENT  HC1  SOLUTION 

DRY,  WEIGH  AND   EXTRACT  WITH 
HOT  WATER 

Ppt.  (Fract.  1)  : 

Filtrate  (Fract.  2)  : 

Filtrate  (Fract.  3): 

Residue  (Fract.  4)  : 

Lipoids 

Organic  extrac- 
tives 
Inorganic  consti- 
tuents 

Organic  extrac- 
tives 
Inorganic  consti- 
tuents 

Proteins 

Organic  extractives  in  Fraction  2  and  3  are  equal  to  total  organic  ex- 
tractives. 

Inorganic  constituents  in  Fraction  2  and  3  are  equal  to  total  inorganic 
constituents. 

Fraction  1  and  2  are  soluble  in  alcohol  (85-95  per  cent). 

Fraction  3  is  insoluble  in  alcohol;  soluble  in  hot  water. 

Fraction  4  is  insoluble  in  alcohol  and  hot  water. 

For  a  clearer  understanding  of  the  terms  used  in  this  series 
of  papers,  the  following  interpretation  of  the  chemical  nature, 
anatomical  distribution,  and  physiological  significance  of  the  sub- 
stances determined,  with  special  reference  to  the  nervous  system 
based  both  on  the  studies  already  made  and  those  presented  in 
this  paper,  is  given  below. 

Proteins. 

Chemistry.  These  represent  complex  combinations  of  ammo-acids  ren- 
dered insoluble  in  water  by  coagulation  with  hot  alcohol.  This  fraction 
has  been  exhaustively  extracted  with  hot  alcohol  and  should  retain  only 
traces  of  lipoids  and  fats.  The  nucleoproteins  and  the  neurokeratin  are 
included  in  this  fraction. 

Anatomical  distribution.  In  the  part  of  the  nervous  system  rich  in  cells 
(cortex)  the  proportion  of  the  proteins  is  larger  than  in  the  white  matter. 
Some  of  the  nucleoproteins  are  supposed  to  be  associated  with  the  chro- 
matin  and  Nissl  substance  of  the  nerve  cell.  The  remainder  of  the  nucleo- 
proteins are  represented  by  the  nuclei  of  the  glia  cells  scattered  through- 


3  Although  ether  is  used  in  the  extraction  following  the  first  alcohol,  it 
does  not  remove  any  considerable  amount  of  material  and  need  not  be  con- 
sidered in  the  above  scheme. 


W.  Koch  and  M.  L.  Koch  427 

out  the  nervous  system.  Neurokeratin  occurs  in  the  medullated  sheath 
of  the  nerve  fiber.  The  other  proteins  occur  in  the  axon  of  the  nerve  fiber 
as  well  as  in  the  cell  body  and  its  dendrites. 

Physiological  significance.  The  proteins  have  usually  been  considered 
as  the  essentially  living  part  of  the  protoplasm,  but  some  of  them,  like 
neurokeratin,  are  undoubtedly  inactive  and  represent  supporting  struc- 
tures. The  same  may  be  said  of  the  proteins  which  make  up  the  fibers 
of  the  glia  cells.  It  is  therefore  impossible  to  tell  at  the  present  time  to 
just  what  extent  and  in  what  proportion  the  proteins  are  involved  in  the 
chemical  activities  of  the  nervous  system.  The  significance  of  the  neutral 
sulphur  compounds,  which  represent  simpler  cleavage  products  of  the 
larger  protein  aggregates,  will  be  discussed  later  as  having  an  important 
bearing  on  this  point  (see  p.  431). 

Phosphatides. 

Chemistry.  These  represent  complex  combinations  of  fatty  acids,  phos- 
phoric acid,  glycerin,  and  nitrogen  complexes  of  the  nature  of  choline, 
and  include  among  other  things  lecithin  and  kephalin.  The  chemistry  of 
this  group  is  very  much  in  need  of  revision,  as  some  of  its  members  are 
not  so  simple  as  the  older  work  of  Hoppe-Seyler  has  led  us  to  infer.  The 
group  does  not  include  lecithin  in  combination  with  sulphur  or  cerebrin. 
The  phosphatides  as  here  given  are  calculated  from  the  phosphorus  of 
the  lipoid  fraction  on  the  assumption  that  they  have  an  average  molecular 
weight  of  800.  Correction  must  be  made  for  the  phosphorus  of  the 
sulphatides.4 

Anatomical  distribution.  Comparison  of  cortex  and  corpus  callosum5  in- 
dicates that  the  phosphatides  are  not  very  differently  distributed  between  cell 
body  and  nerve  fiber.  Analyses  of  the  brain  at  a  period  when  medullation 
has  not  begun,  but  when  the  cell  processes  are  growing  freely,  indicate 
that  the  phosphatides  are  largely  associated  with  the  axon.  If  mitochon- 
dria consist  largely  of  phosphatides,  as  has  been  suggested,  the  observa- 
tions of  Cowdry  would  give  us  a  picture  of  their  distribution  in  the  cell 
body.  The  absence  of  mitochondria  in  the  axon,  which  is  known  to  con- 
tain phosphatides,  would  not  argue  against  this,  as  there  is  some  evidence 
that  the  phosphatides  of  the  processes  and  the  cell  body  are  different  in 
their  behavior. 

Physiological  significance.  The  phosphatides,  like  the  proteins,  may  be 
considered  to  be  intimately  associated  with  the  vital  processes  of  the  living 
protoplasm.  Their  colloidal  nature  and  relation  to  inorganic  ions,  as  well 

4  Calculations  for  phosphatides.    The  total  lipoid  phosphorus  found  times 
25.77  gives  the  phosphatides,  on  the  basis  that  3.88  per  cent  of  the  phospha- 
tides consist  of  phosphorus.    Since  51.2  per  cent  of  the  sulphatides  are  phos- 
phatides, that  amount  was  deducted  from  the  total  phosphatides  found. 
The  difference  was  considered  as  free  phosphatides. 

5  Koch,  W.:  Amer.  Journ.  of  Physiol,  xi,  pp.  326-328,  1904. 


428         Chemical  Differentiation  of  the  Brain 

as  their  instability  towards  heat,6  lend  support  to  this  idea.  They  prob- 
ably occur  largely  in  the  cytoplasm,  cell  body  and  its  branches,  where  they 
may  act  as  oxygen  carriers,  as  has  been  suggested  by  the  work  of  Koch 
and  Mostrom.7 

Cerebrosides. 

Chemistry.  Complex  combinations  of  fatty  acids,  galactose,  and  possi- 
bly other  hexoses  with  a  nitrogen  complex  of  the  nature  of  sphingosine. 
The  cerebrosides  are  calculated  from  the  lipoid  sugar  on  the  assumption 
that  they  yield  on  hydrolysis  21.8  per  cent  of  reducing  sugar,  the  amount 
found  by  Thierfelder  in  his  cerebron.  Correction  must  be  made  for  the 
cerebrin  content  of  the  sulphatides.8 

Anatomical  distribution.  Although  the  cerebrosides  are  occasionally 
met  with  in  other  tissues,  they  occur  in  largest  amount  in  the  medullated 
nerve  fiber,  and  their  quantity  increases  as  medullation  proceeds.  The 
rather  large  amount  found  in  the  cortex9  on  chemical  analysis  indicates 
that  they  may  predominate  in  the  fibers  of  that  region. 

Physiological  significance.  As  laid  down  in  the  medullated  nerve  fiber, 
the  cerebrosides  most  probably  serve  only  a  mechanical  function  and  are 
not  available  as  sources  of  energy  in  spite  of  their  carbohydrate  and  fatty 
acid  content. 

Sulphatides. 

Chemistry.  These  represent  the  combination  of  a  phosphatide  with  a 
cerebroside  by  means  of  a  sulphuric  acid  group  in  ester  combination.10 
The  sulphatides  are  estimated  from  the  lipoid  sulphur  on  the  basis  of  a 
sulphur  content  of  2  per  cent,  based  on  the  analysis  of  a  purified  compound.11 

6  Koch,  W  and  Koch,  M.  L. :  this  Journal,  xiv,  pp.  281-282,  1913. 

7  Koch,  W  and  Mostrom,  H.  T. :  Journ.  of  Pharm.  and  Exp.  Ther.,  ii,  No. 
3,  p.  265,  1910. 

8  Calculations  for  cerebrosides.     The  cerebrosides,  from  the  lipoid  frac- 
tion, on  hydrolysis  for  twenty-four  hours  with  a  weak  solution  of  HC1 
(75  cc.  of  water  containing  3  cc.  concentrated  HC1),  yield  21.8  per  cent 
by  weight  galactose.    The  calculations  for  cerebrosides  were  made  on  the 
assumption  that  galactose  and  glucose  were  equivalent  in  reducing  power 
and  the  weight  of  galactose  was  thus  determined  from  Munson  and  Walker's 
tables  for  glucose.     (Journ.  Amer.  Chem.  Soc.,  xxviii,  p.  663) .     The  corrected 
weight  of  total  galactose  to  cerebrosides  was  then  made  on  the  basis  that 
21.8  per  cent  of  the  latter  is  galactose.     Finally  since  42.9  per  cent  of  the 
sulphatides  consist  of  cerebrosides  this  amount  was  deducted  from  the 
total  cerebrosides  found.     The  difference  was  considered  as  cerebrosides. 

9  Koch,  W.  and  Mann,  S.  A. :  Archives  of  Neurology  and  Psychiatry,  iv, 
p.  33,  1909. 

10  Koch,  W.:  Zeitschr.f.  physiol  Chem.,  Ixx,  p.  94,  1910. 

11  Calculations  for  sulphatides.     These  are  considered  to  be  of  the  gen- 
eral formula: 


W.  Koch  and  M.  L.  Koch  429 

If  it  were  desirable  to  recognize  the  chemical  identity  of  the  much  abused 
protagon,  the  sulphatides  might  be  considered  as  purified  products.  Pro- 
tagon  could  be  much  more  safely  calculated  from  the  lipoid  sulphur  than 
from  the  lipoid  sugar  as  Noll12  has  attempted.  The  sulphur  content  of 
protagon  preparations,  when  it  has  not  been  simply  ignored,  is  variously 
reported  as  0.5  and  1.0  per  cent. 

Anatomical  distribution.  The  sulphatides,  like  the  cerebrosides,  increase 
parallel  with  the  growth  of  the  medullary  sheath  and  may  be  considered 
as  essential  constituents  of  that  structure.  The  fact  that  the  sulphatides, 
as  the  result  of  more  recent  work,  have  been  found  to  be  pretty  generally 
distributed  in  other  tissues,  indicates  that  they  might  occur  in  the  cell 
body  of  the  neurone,  although  a  comparison  of  the  analyses  of  cortex  and 
corpus  callosum  does  not  make  this  very  probable.  The  sulphatides  have 
an  important  function  in  the  maturing  of  the  nerve  fiber  and  give  the 
Weigert  staining  reaction  in  a  very  characteristic  manner. 

Physiological  significance.  Their  colloidal  nature  and  the  peculiar  com- 
bination into  which  the  sulphatides  enter  with  potassium,  suggests  that 
they  may  have  an  important  relation  to  the  nerve  impulse  and  to  the  phe- 
nomena of  conductivity  in  general. 

Organic  extractives  and  inorganic  constituents. 

Chemistry.  This  group  represents  essentially  the  water-soluble,  non- 
colloidal  constituents  of  the  nervous  system.  The  older  method  of  esti- 
mating the  inorganic  constituents  by  the  ash  has  been  abandoned  as  too 
inaccurate.  The  principal  reason  for  reporting  the  above  group  is  to  give 
an  idea  of  the  ratio  between  the  colloidal  and  non-colloidal  constituents. 

Anatomical  distribution.  The  group  occurs  in  large  quantity  in  the 
cell  body,  although  some  is  also  present  in  the  axon  of  the  nerve  fiber. 

Physiological  significance.  This  group  is  a  rough  index  of  the  amount 
of  metabolic  activity  going  on  in  the  tissue,  as  it  represents  at  the  same 
time  the  end  products  of  chemical  activity,  as  well  as  the  culture  media 
from  which  the  more  complex  combinations  are  built  up. 

Undetermined  (cholesterol). 

This  fraction  is  represented  in  the  nervous  system  to  a  certain  extent 
by  cholesterol,  which  has  not  been  directly  estimated.  Besides  this,  how- 


O 

II 
(Phosphatides)  x  — O — S — O —  (Cerebrosides)  y 

II 

O 

containing  2.0  per  cent  sulphur,  42.9  per  cent  cerebrosides,  and  51.2  per 
cent  phosphatides.     Then  we  have, 

(Lipoid  sulphur  X  50)     =         ^  rf  su,  hat;des  ;n  dry  substance. 
weight  of  dry  substance 

12  Noll,  A. :  Zeitschr.  f.  physiol.  Chem.,  xxvii,  p.  370,  1899. 


43O         Chemical  Differentiation  of  the  Brain 

ever,  all  the  errors  of  analysis,  as  well  as  of  such  calculations  as  are  based 
on  assumed  factors,  enter  into  this  fraction.  After  accounting  for.  the 
cholesterol  in  the  brain  of  the  50  and  100  mm.  pig  fetus,13  in  which  this 
was  estimated  directly  by  Mendel,  there  remained  undetermined  2  to  3 
per  cent  of  the  total  solids.  Considering  the  number  of  groups  estimated, 
this  is  not  a  very  discouraging  result.  (In  other  tissues,  which  contain 
little  cholesterol,  the  undetermined  is  recorded  as  neutral  fat.) 

Anatomical  distribution.  Cholesterol  is  principally  of  interest  as  a  con- 
stituent of  the  medullary  sheath  to  which  it  adds  a  sort  of  mechanical 
stability.  But  it  is  present  in  the  cell  bodies  also,  possibly  contributing 
to  the  cell  membranes.  According  to  Lorrain  Smith14  it  is  one  of  the  sub- 
stances responsible  for  the  color  which  the  medullary  sheath  gives  with 
Weigert's  stain. 

Total  sulphur  and  total  phosphorus. 

It  may  not  be  out  of  place  to  state  briefly  the  reasons  for  selecting  these 
two  elements  for  special  determination  in  preference  to  others.  As  far 
as  the  phosphorus  is  concerned,  the  importance  of  the  nucleins  to  all  liv- 
ing cells  and  the  phosphatides  to  the  nervous  system  in  particular,  amply 
justify  its  selection.  The  reason  for  selecting  sulphur  in  preference  to 
the  much  more  generally  studied  nitrogen,  may,-  however  need  a  word  of 
explanation. 

Nitrogen  is  studied  for  two  reasons:  because  it  is  an  important  element 
in  the  building  up  of  the  proteins,  and  because  it  is  easy  of  estimation. 

Sulphur  is  just  as  characteristic  of  proteins,  in  fact  more  so,  as  it  does 
not  enter  into  the  non-protein  groups  such  as  the  nucleic  acids.  Among 
the  lipoids,  too,  sulphur  enters  into  only  one  group,  the  sulphatides,  while 
nitrogen  occurs  in  all  except  cholesterol. 

In  other  words,  to  estimate  sulphur  in  the  protein  fraction  is  to  esti- 
mate an  element  essentially  characteristic  of  the  more  truly  protein  part. 
To  estimate  it  in  the  lipoid  fraction,  enables  one  to  distinguish  one  par- 
ticurar,  and,  as  growth  curves  show,  a  very  interesting  group  of  lipoids. 
Besides,  as  has  already  been  pointed  out  in  a  previous  paper15  sulphur 
occurs  in  the  tissues  in  several  states  of  oxidation  and  thus  gives  us  some 
indication  of  the  intensity  of  reactions  of  oxidation  which  are  so  impor- 
tant to  growing  tissues,  and  about  which  we  know  so  little.  It  seems  wise 
therefore  to  estimate  the  sulphur,  and  in  case  there  are  any  special  reasons 
to  study  nitrogen,  to  study  it  rather  in  the  form  of  one  of  its  definite 
groups  of  compounds  such  as  the  purine  bases  or  the  amino-acids. 


13  Koch,  Mathilde  L. :  this  Journal,  xiv,  pp.  267-279,  1913. 

14  Smith,  Lorrain:  Journ.  of  Path,  and  Bact.,  xv,  pp.  179-181,  1911. 

15  Koch,  W.  and  Upson,  F.  W. :  Proc.  Soc.  for  Exp.  Biol.  and  Med.,  vii, 
pp.  5-6,  1909. 


W.  Koch  and  M.  L.  Koch 


Distribution  of  sulphur. 

Chemistry.  PROTEIN  S.  This  group  represents  sulphur  in  various  amino- 
acid  combinations  such  as  cystine  or  cysteine.  The  proteins  in  which  this 
sulphur  fraction  is  found  have  been  coagulated  and  rendered  insoluble  in 
water  by  treatment  with  hot  alcohol. 

LIPOID  S.  Ethereal  sulphuric  acid  combinations  are  discussed  under 
sulphatides. 

NEUTRAL  S.  This  group  of  compounds  represents  the  total  non-col- 
loidal, water-soluble  combinations  of  sulphur,  minus  the  inorganic  sul- 
phates. As  far  as  studied,  they  resemble  in  all  their  reactions  a  similar 
group  found  in  the  urine  and  called  by  Bondzynski  proteinic  acids.  They 
represent,  probably,  larger  cleavage  products  of  the  protein  molecule  or 
complex  non-coagulable,  water-soluble  polypeptides  somewhat  altered 
by  processes  of  oxidation.  The  sulphur  of  this  fraction  is  represented 
essentially  by  compounds  included  among  the  organic  extractives,  and 
the  sulphur  is  most  often  in  an  oxidized  form  like  taurine  or  ethereal 
sulphate. 

INORGANIC  S  (inorganic  sulphates).  Derivatives  of  sulphur  directly 
precipitated  by  barium  chloride  in  hydrochloric  acid  solution. 

Anatomical  distribution  and  physiological  significance.  The  LIPOID  S, 
as  has  already  been  mentioned  under  the  sulphatides,  represents  an  essen- 
tial constituent  of  the  medullary  sheath.  The  proportion  in  which  it 
occurs  in  the  sheath  can  be  considered  as  a  measure  of  the  maturity  of 
the  sheathing  substance. 

THE  PROTEIN  S  AND  NEUTRAL  S  will  be  considered  together  as  they  bear 
an  important  relation  to  one  another  and  as  the  combinations  in  which 
they  occur  are  essential  constituents  of  all  living  cells.  As  has  already 
been  stated,  the  study  of  these  two  groups  of  sulphur  compounds  gives 
us  a  means  of  investigating  the  protein  metabolism  of  the  central  nervous 
system  during  its  growth  period. 

TABLE  I. 

A  comparison  of  neutral  sulphur  with  protein  sulphur  in  the  brain  of  the  albino 
rat  at  different  ages  (figures  in  per  cent  of  total  sulphur}. 


PROTEIN  SULPHUR 

NEUTRAL  SULPHUR 

1  day                                 

30.5 

48.2 

10  days                                   

44.2 

45.4 

20  days 

56.4 

28.6 

40  days            .             

63.7 

18.2 

120  days            .               

61.8 

18.7 

210  days                               .    ... 

63.8 

14.5 

During  the  early  stages  when  growth  is  proceeding  rapidly  and  chem- 
ical activities  may  be  considered  to  be  at  their  height,  the  proportion  of 


432          Chemical  Differentiation  of  the  Brain 

non-colloidal,  relatively  smaller,  neutral  sulphur  molecules  is  at  a  maxi- 
mum. This  is  what  we  should  expect  when  we  consider  living  matter 
not  as  a  collection  of  highly  organized  molecules,  but  rather  as  a  hetero- 
geneous substratum  in  which  relatively  smaller  molecules  or  their  dissoci- 
ated products  are  engaged  in  chemical  transformations.  As  the  tissues 
grow  and  become  more  highly  differentiated  and  mature,  more  and  more 
protein  is  laid  down  as  structural  material,  and  the  proportion  is  shifted  . 
in  the  direction  of  the  protein  sulphur.  A  comparison  of  the  cortex  of 
the  human  at  two  years  and  at  maturity  illustrates  this  point.16 

2  years'  cortex Protein  S,  63;  Neutral  S,  22. 

19  years'  cortex Protein  S,  73;  Neutral  S,  12. 

The  change  suggests,  therefore,  a  decrease  in  chemically  active  mate- 
rial associated  with  the  increasing  complexity  of  the  tissue.  Such  data 
as  we  have  at  hand  indicate  that  we  have  in  the  protein  sulphur  and  neu- 
tral sulphur  ratio  a  valuable  means  of  measuring  the  relative  growth 
intensity  of  the  nervous  system  at  different  periods  during  its  development 
after  the  state  of  cell  division  has  practically  ceased. 

There  might  be  another  way  of  measuring  this  intensity  of  chemical 
activity,  namely,  by  means  of  the  inorganic^  sulphates,  which  represent 
the  end  products  and  the  final  state  of  oxidation  of  the  compounds  involved 
in  these  reactions,  but  they  are  eliminated  rather  easily  from  the  cell,  and 
it  is  therefore  difficult  to  attach  any  significance  to  their  variations. 

Distribution  of  phosphorus. 

Chemistry.  PROTEIN  P.  This  group  represents  phosphorus  largely  in 
combination  as  nucleic  acid.  In  the  nervous  system  this  nucleic  acid  is 
combined  with  such  a  very  large  amount  of  protein17  that  the  per  cent  of 
phosphorus  in  the  resulting  nucleoprotein  drops  to  0.57  per  cent  as  com- 
pared with  3  to  4  per  cent  in  such  a  tissue  as  the  pancreas. 

LIPOID  P.    Already  discussed  under  phosphatides. 

WATER-SOLUBLE  P.  This  group  includes  non-colloidal,  water-soluble 
organic  combinations  of  phosphoric  acid  and  inorganic  phosphates.  On 
account  of  the  relative  ease  with  which  the  organic  extractive  combina- 
tions of  this  form  of  phosphoric  acid  break  down,  it  is  difficult  to  estimate 
the  proportion  which  is  in  organic  combination.  The  results  which  are  so 
far  recorded  represent,  therefore,  rather  the  possible  maximum,  than  a 
very  close  approach  to  the  actual  value.  (See  articles  of  Grindley,18  Trow- 
bridge,19  and  Forbes.20) 

16  Koch,  W.  and  Mann,  S.  A.:  Journ.  of  PhysioL,  xxxvi,  p.  2,  1907. 

17  Also  accounts  for  poor  staining  reaction  of  neurone  nucleus. 

18  Grindley:  Journ.  of  Amer.  Chem.  Soc.,  xxviii,  pp.  25-63,  1906. 

19  Trowbridge,  P.  F.  and  Francis,  C.  K.:  This  Journal,  vii,  pp.  481-501, 
1910. 

20  Forbes,  E.  B. :  Ohio  Agric.  Exp.  Sta.  Bulletin  215,  1910,  pp.  459-489. 


W.  Koch  and  M.  L.  Koch  433 

Anatomical  distribution  and  physiological  significance.  The  protein  phos- 
phorus is  largely  associated  with  the  nucleic  acid  of  the  nucleus.  In  the 
nervous  system  it  is  also  supposed  to  be  associated  with  the  Nissl  sub- 
stance, but  this  is  still  a  doubtful  matter.  The  accuracy  with  which  we 
can  estimate  nuclear  material  in  the  anatomical  sense  from  such  a  figure 
as  the  protein  phosphorus  is  difficult  to  determine,  as  there  are  three 
complicating  factors. 

1.  The  possibility  that  the  nucleus,  as  an  anatomical  unit,  contains 
other  compounds  besides  nucleoproteins. 

2.  The  fact  that  nucleic  acid  itself  may  be  associated  with  very  widely 
varying  quantities  of  protein. 

3.  The  possibility  that  substances  yielding  a  protein  phosphorus  frac- 
tion may  occur  in  the  cytoplasm. 

Observations  by  Miescher21  on  the  sperm,  however,  very  strongly  sug- 
gest that  protein  phosphorus  is  largely  associated  with  the  nucleus,  while 
lipoid  phosphorus  is  largely  associated  with  the  cytoplasm. 

As  regards  the  water-soluble  phosphorus,  the  principal  point  of  interest, 
just  as  in  the  case  of  the  neutral  sulphur,  is  its  ratio  to  the  protein  or  col- 
loidal forms  of  phosphorus.  Thus  in  a  study  on  a  lower  plant  form  (Asper- 
gillus  niger]  Koch  and  Reed22  could  demonstrate  that  under  extreme  con- 
ditions, such  as  can  only  be  realized  with  plant  material,  it  is  possible  to 
carry  the  growth  processes  to  such  a  point  that  all  the  non-colloidal, 
water-soluble  phosphorus  is  converted  into  colloidal  combinations.  At 
such  a  point  the  growth  of  the  plant  comes  to  a  stop. 

The  function  of  the  inorganic  phosphates  in  maintaining  the  neutrality 
of  protoplasm  as  suggested  by  Henderson23  is  also  a  point  of  interest, 
although  of  less  importance  to  the  nervous  system  than  to  muscle  tissue. 

Inorganic  constituents. 

Chemistry.  The  inorganic  constituents  found  in  the  nervous  system  are 
the  cations  Na,  K,  Ca,  Mg,  Fe,  and  the  anions  Cl,  SO4,  P04. 

In  the  method  devised  for  this  study  the  usual  method  of  estimating 
these  constituents  by  the  ash  was  abandoned  on  account  of  the  fact  that 
by  the  process  of  ashing,  the  relation  of  cations  to  anions  is  profoundly 
altered.  As  a  result  of  this  precaution,  the  interesting  fact  has  been 
clearly  demonstrated  that  a  large  proportion  of  the  cations,  especially 
sodium  and  potassium,  occur  combined  with  complex  anions,  sometimes 
colloidal  in  nature. 

The  work  of  Pike*4  has  brought  to  light  the  interesting  point  that  in 
the  nervous  system  the  sodium  and  potassium,  more  especially  the  latter, 

21  Miescher,  F. :  Hoppe-Seyler's  Med.-chem.  Unters.,  p.  452. 

22  Koch,  W.  and  Reed,  H.  S.:  this  Journal,  iii,  p.  49,  1907. 

23  Henderson,  L.  J. :  this  Journal,  vii,  pp.  29-35,  1910. 

24  Koch,  W.  and  Pike,  F.  H.:  Journ.  of  Pharm.  and  Exp.  Ther.,  ii,  pp. 
245-248,  1910. 

THE   JOURNAL   OF    BIOLOGICAL   CHEMISTRY,    VOL.   XV,    NO.   3 


434         Chemical  Differentiation  of  the  Brain 

are  combined  with  such  lipoids  as  the  sulphatides  and  kephalines  (a  sub- 
group of  phosphatides),  while  the  Ca  and  Mg  have  more  tendency  to  remain 
combined  with  the  proteins. 

Anatomical  distribution  and  physiological  significance.  Very  little  is 
known  of  the  anatomical  distribution  of  the  salts  except  as  shown  by  the 
work  of  Macallum25  which  demonstrates  that  chlorides  and  potassium  are 
associated  with  the  nerve  fiber.  According  to  Alcock,26  potassium  is  sup- 
posed to  play  an  important  role  in  the  propagation  of  the  nerve  impulse. 

With  this  introductory  statement  of  the  anatomical  distribu- 
tion and  physiological  significance  of  the  substances  quantitatively 
determined,  we  may  now  present  the  results  of  a  study  of  their 
variation  during  the  growth  of  the  brain. 

The  brain  of  the  albino  rat  was  selected  for  this  study,  for  the 
reasons  already  presented  in  the  first  paper  of  this  series.27 

From  a  comparison  of  the  brain  of  the  albino  rat  at  birth  and 
the  brain  of  the  fetal  pig,  it  was  found  that  the  brain  of  the  new 
born  rat  is  as  young  nervous  material  as  can  conveniently  be 
analyzed  at  present.  It  forms  therefore  a  suitable  starting  point 
for  this  study  of  chemical  differentiation  during  growth.  The 
analyses  reported  in  this  paper  are  those  of  the  brains  of  rats 
aged  respectively,  1,  10,  20,  40,  120,  and  210  days.  The  results 
show  that  it  was  possible  to  follow  closely  the  various  structural 
changes  which  occur  during  the  differentiation  of  the  growing 
nervous  system 

The  material  was  furnished  by  the  Wistar  Institute  of  Anatomy; 
the  brains  being  collected  and  analyzed  in  the  manner  already 
detailed.28  Koch's  quantitative  methods  were  used.29 

RESULTS   OF  ANALYSES. 

The  results  of  analyses  are  embodied  in  Table  II.  Duplicate 
analyses  have  been  carried  on  throughout,  and  are  summarized 
in  Table  III.  This  table  gives  the  averages  of  the  analyses,  except 

25  Macallum,  A.  B. :  Journ.  ofPhysioL,  xxxii,  pp.  95-128, 1905;  Macallum, 
A.  B.  and  Menten,  M.  L. :  Report  75th  Meeting  British  Assoc.  Adv.  Sti., 
p.  555,  1906. 

26  Alcock,  N.  H.:  Journ.  of  Physiol.,  xxxix,  pp.  402-410,  1911. 

27  Koch,  Mathilde  L. :  this  Journal,  xiv,  pp.  267-279,  1913. 

28  Koch,  Mathilde  L.:  loc.  cit. 

29  Koch,  W.:  Journ.  of  Amer.  Chem.  Soc.,  xxxi,  pp.  1335-1364,  1909. 


W.  Koch  and  M.  L.  Koch  435 

in  two  instances  where  the  value  from  one  analysis  only  is  pre- 
ferred: Table  IV  gives  the  absolute  weights  of  these  constituents, 
as  found  in  one  brain;  while  Table  V  gives  the  ratio  of  increase 
of  the  different  constituents,  taking  the  amount  of  each  constitu- 
ent in  the  brain  of  the  rat  at  birth  to  be  unity  and  determining 
the  number  of  times  each  constituent  had  increased  at  successive 
ages  from  birth  to  maturity.  For  comparison  there  is  given  in 
Table  II  one  analysis  of  the  spinal  cord  at  120  days. 

DISCUSSION   OF  RESULTS. 

The  growth  of  the  nervous  system  from  the  first  laying  down 
of  the  neural  canal  to  maturity  may  be  divided  into  four  periods. 
The  first  period,  during  which  cell  division  is  the  most  charac- 
teristic feature,  lasts  to  about  birth.  A  short  time  before  birth 
cell  division  begins  to  decrease.  The  chemical  changes  during 
this  first  period  were  not  studied  directly  in  the  albino  rat  for 
the  reasons  stated  in  the  first  paper30  but  the  composition  of  the 
nervous  system  in  this  primitive,  undifferentiated  state  may  be 
seen  in  the  analysis  of  the  fetal  pig  brain  reported  in  the  first 
paper  of  the  series.  At  this  time  phosphatides  are  present,  sul- 
phatides  are  relatively  less  important  and  cerebrosides  are  en- 
tirely lacking;  proteins,  phosphatides,  extractives,  salts  and  water 
are  the  predominant  constituents  of  the  tissue. 

The  second  period  (see  Table  VI)  lasts  from  birth  for  about 
ten  days,  when  the  third  period  begins.  The  second  period  is 
characterized  structurally  by  the  development  of  fibers  from  the 
cells  and  the  increase  in  their  size.  Donaldson  has  estimated 
that  the  number  of  nerve  cells  does  not  increase  more  than  3  to 
6  per  cent  during  this  period,  but  the  cells  do  add  to  the  number 
and  size  of  their  branching  processes.  This  period,  as  may  be 
seen  from  Table  VI,  is  one  of  intense  growth  of  all  the  solid  con- 
stituents. The  proteins  continue  throughout  this  period  to  be 
formed  at  a  very  rapid  rate,  4-5  mgms.  being  laid  down  per  day. 
Cerebrosides  are  either  absent  entirely,  or  present  in  very  small 
quantities. 

In  the  third  period,  that  of  most  rapid  growth,  from  the  tenth 
to  the  twentieth  day,  medullation  begins.  There  is  a  wonderful 

30  Koch,  M.  L. :  this  Journal,  xiv,  p.  279,  1913. 


436         Chemical  Differentiation  of  the  Brain 


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438         Chemical  Differentiation  of  the  Brain 


TABLE  III. 


The  relative  proportions  of  the  constituents  of  the  brain  of  the  albino  rat  at 
different  ages  (averages  from  Table  II) . 


AGE  IN   DAYS 

1 

10 

20 

40 

120 

210 

Moist  weight  of  one  brain  in  grams  .  . 
Solids  in  per  cent  

0.25* 
10.42 
0.026 
100 

0.86f 
12.5 
0.107 
40 

1.28* 
17.5 
0.224 
54 

1.38* 
20.34 
0.281 
35 

1.60* 
21.65 
0.347 
30 

1.67f 
21.9 
0.365 
31 

Dry  weight  of  one  brain  in  grams.  .  .  . 
Number  of  brains  in  each  sample  

Laboratory  Number  

W.16,24 

W.40 

W.  17,  25 

W.28,29 

W.7,8 

W.  13 

Constituents  in  per  cent  of  total  solids. 


Proteins  

58.25* 

56.  5f 

53.3* 

48.4* 

47.6* 

48.  5  1 

Phosphatides  

15  2 

12.3 

21  4 

21  8 

21  6 

22.0 

Cerebrosides 

3  0 

5  9 

8  4f 

8  41 

Sulphatides  

1  45 

2.6 

2  5 

2  55 

3  55 

4  5 

Organic  extractives                          \ 

Inorganic  constituents  '  / 
Cholesterol  (undetermined)  §  
Total  sulphur 

17.9 

7.2 
1  00 

15.1 

13.5 
0  83 

14.55 

5.25 
0  70 

14.85 

6.5 
0  55 

9.75 

9.1 
0  56 

9.8| 

6.8 
0  58 

Total  phosphorus  

1  87 

1.48 

1  66 

1  52 

1  42 

1  39 

Distribution  of  sulphur  in  per  cent  of  total  S. 


Protein  S  

30  5 

44  2 

56  4 

63  75 

61  8 

63  8 

Lipoid  S  . 

3  0 

6  1 

7  1 

9  65 

12  7 

15  6 

NeutralS  . 

48  2 

45  4 

28  6 

18  15 

18  7 

14  5 

Inorganic  S  

18  3 

4  3 

7  9 

8  45 

6  8 

6  1 

Distribution  of  phosphorus  in  per  cent  of  total  P. 


Protein  P  

13  3 

13  45* 

5  9 

8  7 

7  3 

6  8 

Lipoid  P  

33  2 

34  95 

52  85 

57  3 

64  1 

67  6 

Water  sol.  P  

53  5 

51  6 

41  25 

34  0 

28  6 

25  6 

*  Record  from  average  duplicate  analyses, 
t  Record  from  one  analysis  only. 
J  Taken  from  analysis,  W.  8. 
§  Obtained  by  difference. 


W.  Koch  and  M.  L.  Koch 


439 


TABLE  IV. 


Absolute  weights,  in  milligrams,  of  the  constituents  of  a  single  brain  of  the 
albino  rat  at  different  ages  (prepared  from  Table  HI) . 


AGE  IN   DAYS 

1 

10 

20 

40 

I  20 

210 

Moist  weight  of  one 

brain  in  grams  

0.25 

0.86 

1.28 

1.38 

1.60 

1.67 

Solids  in  per  cent  .  .  . 

10.42 

12.5 

17.5 

20.34 

21.65 

21.9 

Dry  weight  of  one 

brain  in  grams  

0.026      0.107 

0.224 

0.281 

0.347 

0.365 

Laboratory  Number  

W.16,24 

W.  40 

W.  17,  25 

W.  28,  29 

W.  7,  8 

W.  13 

Absolute  weights  in  milligrams. 


Proteins  (1)J  , 

15.14* 

60.45f 

119.4* 

136.0* 

165.2* 

177.  Of 

Phosphatides  (2)  ... 

3.95 

13.16 

47.9 

61.3 

74.95 

80.3 

Cerebrosides  (3)  

6.7 

16.6 

29.15 

30.66 

Sulphatides  (4)  

0.38 

2.78 

5.6 

7.2 

12.3 

16.4 

Organic  extrac-     ] 

tives  
Inorganic  constit- 

4.65 

16.16 

32.6 

41.7 

33.8 

35.8 

uents  

Cholesterol  unde-1 
termined  (5)  / 

1.87 

(14.45) 

11.7 

18.2 

31.6 

24.8 

Total  sulphur 

0.26 

0.90 

1.57 

1.54 

1.94 

2.12 

Total  phosphorus.  .  . 

0.48 

1.6 

3.72 

4.30 

4.93 

5.07 

In  absolute  weight  in  milligrams  of  sulphur. 


ProteinS  (IS)  §  
Lipoid  S  (4)  

0.079 
0  008 

0.398 
0.054 

0.885 
0.111 

0.982 
0.149 

1.199 
0.246 

1.352 
0.330 

Neutral  S  (6)  
Inorganic  S  (7)  

0.125 
0.047 

0.409 
0.039 

0.449 
0.122 

0.279 
0.130 

0.363 
0.132 

0.307 
0.129 

In  absolute  weight  in  milligrams  of  phosphorus. 


Protein  P  (IP)  

0  064 

0.215* 

0.220 

0.374 

0.360 

0.345 

Lipoid  P  (2)  

0.161 

0.558 

1.964 

2.464 

3.160 

3.427 

Water  sol.  P  (8).... 

0.260 

0.826 

1.532 

1.462 

1.410 

1.298 

*  Record  from  average  duplicate  analyses. 

t  Record  from  one  analysis. 

t  Figures  in  parentheses  in  this  section  refer  to  Chart  III. 

§  Figures  in  parentheses  in  this  and  the  following  sections  refer  to  Chart  IV. 


440         Chemical  Differentiation  of  the  Brain 


TABLE  V. 


The  ratio  of  the  increase  of  the  constituents  of  the  brain  of  the  albino  rat  at 
different  ages,  taking  the  amount  of  each  constituent  found  in  the  brain  at 
birth  as  unity  (prepared  from  Table  IV). 


AGE  IN 

DAYS 

l 

10 

20 

40 

120 

210 

Total  Solids  

1 

4.0 

8.6 

10.8 

13.3 

14.0 

Proteins  

1 

4.0 

7.9 

9.0 

11.0 

11.7 

Phosphatides  

1 

3.3 

12.0 

15.5 

19.0 

20.3 

Cerebrosides 

Sulphatides  

1 

7.4 

14.8 

19.0 

32.6 

43.5 

Organic  extractives                          1 

Inorganic  constituents.  .                  / 

1 

3.5 

7.0 

8.9 

7.2 

7.7 

Cholesterol  (undetermined)  

1 

7.7 

6.2 

9.0 

16.9 

13.2 

Total  sulphur  

1 

3  4 

6  0 

5  9 

7  4 

8.0 

Total  phosphorus  

1 

3.2 

7.6 

8.8 

10.1 

10.4 

ProteinS  ".  .    . 

5  0 

11  1 

12  3 

15  0 

17.0 

Lipoid  S  .  .  . 

6  9 

14  3 

19  1 

31  5 

42  3 

Neutral  S  

3  3 

3  6 

2.2 

2  9 

2.5 

Inorganic  S  

(1  3) 

2  6 

2  7 

2  8 

2  7 

Protein  P  

4  1 

4  3 

7  2 

7  0 

6  7 

Lipoid  P. 

14  3 

15  3 

19  2 

24  7 

26  8 

Water  sol.  P  

1 

3.9 

7.4 

6.9 

6.8 

6.2 

TABLE  VI. 

Rate  of  growth  (milligrams  formed  per  day)  of  different  constituents  in  a  single 
brain  of  the  albino  rat  at  different  age  periods  (prepared  from  Table  IV). 


2 

3 

4 

Between...                                                                         / 

1-10 

10-20 

20-40 

40-120 

120-210 

I 

days 

days 

days 

days 

days 

Proteins  

4  53 

5  9 

0  84 

0  36 

0  13 

Phosphatides  

0  92 

3  5 

0  67 

0  17 

0  06 

Cerebrosides  

0  49 

0  15 

0  006 

Sulphatides 

0  24 

0  29 

0  08 

0  06 

0  045 

Organic  extractives.  .                                  ) 

Inorganic  constituents  J 

1.51 

1.64 

0.46 

0.00 

0.000 

Cholesterol  (undetermined)  . 

(0  49) 

(0  49) 

0  32 

0  17 

0  000 

AGE  PERIODS 


W.  Koch  and  M.  L.  Koch  441 

outburst  of  activity  in  forming  phosphatides  which  reach  a  max- 
imum rate  of  formation  of  3.5  mgms.  per  day.  This  change  is 
no  doubt  correlated  with  the  great  growth  of  the  fibers  and  the 
beginning  of  medullation.  The  organic  extractives  and  inorganic 
constituents  continue  to  be  formed  at  the  same  rate  since  the 
cell  bodies  are  increasing  in  size;  probably  not  more  than  from 
10  to  20  per  cent  having  reached  anything  approaching  adult 
size  up  to  this  time. 

The  sulphatides,  although  present  in  less  quantity  than  the 
phosphatides,  reach  also  their  maximum  rate  of  formation.  The 
whole  chemical  picture  is  that  of  a  rapid  growth  of  protoplasm, 
with  a  change  in  its  character  owing  to  the  increase  of  phospha- 
tides. During  this  period  the  neurones  increase  rapidly  in  size. 

Attention  is  particularly  directed  to  the  temporary  great  in- 
crease in  neutral  sulphur  during  these  two  periods  of  intense 
growth  (Table  IV).  The  significance  of  this  has  already  been 
discussed  on  p.  431  et  seq. 

The  fourth  growth  period  is  the  period  of  continued  medulla- 
tion. This  period  is  characterized  chemically  by  a  great  reduc- 
tion in  the  rate  of  formation  of  all  substances  except  the  cerebro- 
sides.  These  latter  between  20-40  days  come  into  view,  almost 
equalling  the  phosphatides  and  being  more  than  half  the  amount 
of  the  proteins  formed  at  the  same  time.  The  cerebrosides  con- 
tribute a  large  share  toward  medullation.  The  rate  of  formation 
of  the  various  constituents  per  day  falls  in  the  20-40  day  period, 
as  compared  with  the  10-20  day  period,  in  the  case  of  the  proteins 
to  one-seventh;  the  phosphatides  to  one-fifth;  the  sulphatides  to 
one-third;  and  the  organic  and  inorganic  extractives  to  one-third. 
The  formation  of  the  proteins  decreases  the  most;  the  cerebrosides, 
the  least.  If  the  rate  of  formation  in  the  40-120  day  period  is 
compared  to  that  of  the  10-20  day  period  it  is  seen  that  the 
protein  formation  has  decreased  to  one-sixteenth;  the  phospha- 
tides to  one-twentieth;  the  sulphatides  to  one-fourth  but  are  still 
increasing.  On  the  other  hand,  the  organic  extractives  and  inor- 
ganic constituents  have  not  increased  at  all,  indicating  that  metab- 
olism is  much  reduced  in  its  rate  and  the  growth  of  the  protoplasm 
is  much  slower.  During  this  fourth  period  then,  the  sulphatides 
continue  to  be  formed  at  a  more  rapid  rate,  relative  to  their 
total  amount,  than  any  other  constituents;  and  in  the  120-210 


442         Chemical  Differentiation  of  the  Brain 

day  period,  the  total  sulphatides  formed  surpass  the  cerebrosides, 
nearly  equal  the  phosphatides,  and  are  more  than  one-third  the 
proteins.  The  constant  production  of  sulphatides  is,  therefore, 
a  marked  feature  of  late  medullation,  just  as  that  of  the  phos- 
phatides is  of  the  early  medullation.  The  sulphatides  diminish  in 
their  rate  of  formation  far  less  than  any  other  constituents. 

Finally  we  have  the  period  from  210  days  on:  the  period  of 
stationary  or  adult  life.  We  have  no  definite  chemical  data  as 
to  any  changes  occurring  during  this  period,  but  from  such  data 
at  hand,  as  the  periods  just  studied,  we  can  assume  that  the 
growth  processes  during  adult  life  are  practically  stationary  except 
perhaps  a  very  gradual  increase  in  the  per  cent  of  solids. 

The  enlargement  of  the  brain  may,  therefore,  in  great  part 
be  accounted  for  chemically  by  the  formation  of  the  medullary 
sheath.  Donaldson31  has  found  that  some  88  per  cent  of  the 
volume  of  the  adult  brain  is  composed  of  the  axons  and  their 
sheaths,  while  the  cell  bodies  with  their  dendrites  and  the  sup- 
porting tissues  together  only  make  up  the  remaining  12  per  cent. 
The  axones,  therefore,  medullated  or  non-medullated,  are  mainly 
responsible  for  the  increase  of  the  size  of  the  brain  and  for  the 
changes  which  it  undergoes  during  post  natal  growth.  To  bring 
more  vividly  before  the  eye  the  relative  rate  of  growth  of  the 
various  constituents,  we  have  prepared  Charts  1  and  2  from 
Tables  III  and  IV.  These  charts  are  self  explanatory.  We  have 
also  prepared  Charts  3  and  4,  an  explanation  of  which  is  given 
below. 

Chart  3  shows  the  relation  of  lipoid32  to  protein.  In  this  the 
weights  of  the  several  constituents  are  represented  for  one  brain 
at  each  age.  This  chart  shows  that  while  both  the  proteins  and 
the  lipoids  are  increasing  in  absolute  weight,  the  proportion  of 
lipoid  to  protein  is  becoming  greater  and  greater  as  the  tissue 
grows  older.  This  indicates  that  the  rate  of  increase  for  the 
lipoids  is  greater  than  for  the  proteins  (also  brought  out  in  Table 
VI).  At  120  and  at  210  days  we  find  that  the  lipoids  and  pro- 

31  Donaldson,  H.  H. :  Journ.  of  Nervous  and  Mental  Disease,  xxxviii,  p. 
260,  1911. 

32  Lipoids  here  include  the  phosphatides,  cerebrosides,  and  sulphatides; 
cholesterol,  which  is  classed  as  lipoid,  is  here  recorded  in  the  "undeter- 
mined." 


W.  Koch  and  M.  L.  Koch 


443 


40     50    60    70     80    90     100    110    120    130   140    150 


170    180   190   200  210  220 


CHART  1.  Shows  the  absolute  weight  in  milligrams,  of  the  constituents 
of  a  single  brain  of  the  albino  rat  at  different  ages.  (Age  in  days  along 
the  abscissa;  mgms.  on  the  ordinate.) 


CHART  2.  Shows  the  rate  of  increase  of  the  different  constituents  of 
the  brain  of  the  albino  rat  at  different  ages,  taking  the  amount  of  each 
constituent  in  the  brain  at  birth  as  unity.  (The  ordinate  shows  how  many 
times  the  weight  of  each  constituent  has  increased  over  its  amount  at 
birth  at  the  age  plotted  on  the  abscissa.) 


444         Chemical  Differentiation  of  the  Brain 


150 


100 


50 


Mqros. 


Chart * 

Relations  of 
colloidal  to 
•non-colloidal 
constituents 


Combinations 

°f        - 
Sulphur   .TO 


f  Phosphorus^ 


W.  Koch  and  M.  L.  Koch 


445 


I 

- 

Mqms. 

200 

- 

5 

—  . 

- 

(50 

5 

4 

— 

5 

— 

- 

- 

4 

- 

4 

- 

J 

— 

— 

„ 

100 

S 

3 

3 



4                                      1 

1 

- 

3 

2 

50 

2 

2 

2 

1 

0 

• 

it                                               3 

»r      3 

65  Mqnta.         Spir1 

lai  cord 

40                                             120         210                                120 

Days                           Days    Days                  Days 

l               J     \           \ 

446         Chemical  Differentiation  of  the  Brain 


CHART  3.  Shows,  in  absolute  weight,  the  amounts  of  proteins  and  of 
lipoids  in  the  brain  of  the  albino  rat  at  different  ages.  Based  on  Table 
IV.  1,  Proteins;  £,  Phosphatides ;  3,  Cerebrosides ;  4,  Sulphatides;  5,  Unde- 
termined lipoids  (Cholesterol).  The  organic  extractives  and  inorganic 
constituents  are  not  included.  For  comparison  the  weights  of  the  several 
constituents  in  the  spinal  cord  of  the  albino  rat  at  120  days  are  also  shown; 
the  weight  of  the  dry  substance  of  the  cord  being  taken  as  equal  to  that 
of  the  120-day  brain. 

CHART  4.  Shows,  in  the  albino  rat  at  different  ages,  the  proportional 
values  in  segments  of  a  circle  for  the  sulphur  combinations  (above  the 
equator)  and  for  the  phosphorus  combinations  (below  the  equator) ;  with 
a  further  grouping  into  colloids  and  non-colloids.  Based  -on  Table  IV. 
Again  for  comparison  the  proportional  values  for  the  sulphur  and  the 
phosphorus  combinations  in  the  spinal  cord  of  the  albino  rat  at  120  days 
are  also  given. 

Sulphur  combinations :  1,  Proteins  (protein  sulphur) ;  4,  Sulphatides  (lip- 
oid  sulphur) ;  6,  Neutral  sulphur  (proteic  acids) ;  7,  Inorganic  sulphates. 

Phosphorus  combinations :  1,  Proteins  (protein  phosphorus)  ;#,  Phospha- 
tides (lipoid  phosphorus) ;  8,  Organic  and  inorganic  phosphates  (water  solu- 
ble phosphorus). 

The  colloids  are  represented  by  1  and  4,  of  the  sulphur  combinations 
and  1  and  2  of  the  phosphorus  combinations. 

The  non-colloids  are  represented  by  6  and  7  of  the  sulphur  combinations 
and  by  8  of  the  phosphorus  combinations. 


W.  Koch  and  M.  L.  Koch  447 

teins  are  present  in  the  brain  in  nearly  equal  proportions.  For 
the  sake  of  comparison,  the  corresponding  values  for  the  spinal 
cord  at  120  days  have  been  introduced  into  this  chart. 

To  make  easier  the  comparison  between  the  relations  of  pro- 
teins and  lipoids  in  the  brain  and  in  the  spinal  cord,  it  is  assumed 
for  the  purposes  of  the  chart  that  the  dry  weight  of  the  cord  is 
the  same  as  that  of  the  brain  at  120  days.  Since  the  cord  con- 
tains a  larger  proportion  of  white  matter  than  does  the  brain, 
we  find  that  the  lipoids  in  this  case  predominate  over  the  proteins. 
This  indicates  that  the  chemical  differentiation  during  the  growth 
of  the  nervous  system,  as  recorded  in  this  paper,  is  largely  con- 
cerned with  the  development  of  the  medullated  nerve  fiber. 

Chart  4  shows  very  strikingly  the  great  decrease  with  advanc- 
ing age  in  the  non-colloidal  contrasted  with  the  corresponding 
increase  in  the  colloidal  sulphur  and  phosphorus  compounds. 
Particular  attention  is  called  to  the  neutral  sulphur  which  in  the 
young,  rapidly  metabolizing  tissue  constitutes  the  greater  propor- 
tion of  the  total  sulphur,  whereas  it  becomes  extremely  small  at 
210  days  when  growth  metabolism  is  at  an  end.  Evidently  this 
fraction  may,  with  reserve,  be  considered  an  index  of  growth 
metabolism.  With  advancing  age  the  colloidal,  less  active,  sub- 
stances gradually  crowd  out  the  non-colloidal.  This  is  in  strik- 
ing accord  with  the  interesting  suggestions  of  Child33  that  senes- 
cence is  due  to  the  accumulation  of  these  colloidal  solids,  which 
interpose  resistance  to  metabolism. 

Finally  we  find  the  growth  process  characterized  by  a  steady 
diminution  in  the  proportions  of  water  and  an  increase  in  the  pro- 
portion of  solids.  This  change  is  due  not  alone  to  medullation  in 
the  strict  sense,  since  as  Donaldson34  has  pointed  out  the  decrease 
begins  before  medullation,  between  birth  and  ten  days  in  the  rat. 
He  attributes  it  to  a  rapid  growth  of  the  axone  at  this  time.  Water 
and  the  proportion  of  neutral  sulphur  are  therefore  criteria  of  the 
youthfulness  of  tissue,  while  the  increase  of  lipoid  sulphur  (sul- 
phatides)  is  a  criterion  of  medullation. 


33  Child,  C.  M. :  Archiv.  f.  Entwicklungs-mechanik  d.  Organismen,  xxxi, 
p.  571,  1911. 

34  Donaldson,  H.  H. :  Journ,  of  Neurology  and  Psychology,  xx,  p.  138, 
1910. 


448          Chemical  Differentiation  of  the  Brain 

SUMMARY. 

The  principal  results  of  this  study  may  be  summarized  as  follows : 
Well-marked  and  characteristic  chemical  changes  occur  in  the  rat- 
brain  during  its  growth  and  these  changes  are  obviously  correlated 
with  its  anatomical  differentiation. 

The  principal  chemical  changes  noted  are: 

1.  A  general  decrease  in  the  per  cent  of  water  which  is  not  due 
entirely  to  medullation  since  the  decrease  begins  before  medulla- 
tion  (Donaldson  '10). 

2.  A  diminution  in  the  relative  per  cent  of  protein  in  the  total 
solids  due  to  the  formation  of  a  large  amount  of  lipoid  matter. 

3.  The  lipoids  which  appear  coincident  with  medullation  and  of 
which  the  development  is  pari  passu  with  medullation  are  the  cere- 
brosides  and  sulphatides.    These,  therefore,  are  chiefly  found  in 
the  medullary  sheaths. 

4.  There  is  a  great  outburst  of  phosphatide  formation  at  the 
very  beginning  of  medullation,  but  the  phosphatides  are  present 
also  in  large  amounts  before  medullation.    The  phosphatides  are 
present,  therefore,  in  the  cells  as  well  as  the  sheaths. 

5.  The  extractives  are  present  in  largest  amounts  during  fetal 
and  early  life  when  growth  and  metabolism  are  at  a  maximum. 
Particularly  the  water-soluble,  organic  sulphur  compounds  (neutral 
sulphur)  diminish  relatively  with  age,  while  the  colloidal  sulphur 
increases.  The  relations  of  the  neutral  sulphur  may  be  interpreted, 
therefore,  as  indicating  the  intensity  of  metabolic  activity. 

6.  The  great  increase  of  colloidal  matter  with  age  clearly  indi- 
cates that  this,  in  the  form  of  supporting  structures,  constitutes  a 
relatively  inactive  material  which  presumably  serves  to  localize 
chemical  processes.    The  accumulation  of  this  material  is  probably 
one  factor  producing  the  general  slowing  of  metabolism  character- 
istic of  senescence.    This  would  thus  become  one  cause  of  senes- 
cence as  Child  has  suggested. 


[Reprinted  from  THE  AMERICAN  NATURALIST,  Vol.  XLVIL,  Feb.,  1913.  J 


ADAPTATION  FEOM  THE  POINT  OF  VIEW  OF 
THE  PHYSIOLOGIST1 

PROFESSOR  ALBERT  P.  MATHEWS 

THE  UNIVERSITY  OF  CHICAGO 

I  FEEL  much  ashamed  in  having  to  expose  my  intellec- 
tual nakedness  before  the  members  of  this  society.  When 
I  came  to  this  meeting  I  supposed  that  adaptation,  or  the 
fitness  of  organisms  to  their  environments,  was  a  physio- 
logical truism ;  that  fishes  were  fitted  by  their  structures 
and  functions  to  a  life  in  the  water ;  that  frogs  were  so 
constituted  that  they  could  live  either  on  land  or  in  water ; 
and  I  was  even  so  ignorant  as  to  believe  that  many  struc- 
tures of  a  bird's  body  adapted  it  to  flight.  But  it  appears 
from  the  paper  of  one  of  my  colleagues  that  in  all  of  these 
things  I  was  most  woefully  mistaken. 

I  feel  some  hesitation,  also,  in  appearing  before  a 
society  composed  largely  of  American  students  of  genet- 
ics, for  I  have  no  new  and  confusing  terminology  to  pro- 
pose; and  owing  to  my  ignorance  of  the  language  they 
speak  and  of  the  short-hand  symbols  sometimes  employed, 
I  am,  perforce,  compelled  to  speak  in  ordinary  English 
which  may  be  understood  by  any  one ;  all  of  which,  I  fear, 
must  invest  all  I  have  to  say  with  an  air  of  superficiality, 
or  even  of  simplicity.  I  am  besides  a  confirmed  con- 
servative in  the  matter  of  evolution,  holding  fast  to  the 
explanation  of  adaptation  given  by  Darwin  of  natural 
selection  of  small  variations;  having  little  or  no  con- 
fidence that  genes,  unit  characters,  mutations,  saltations, 
allelomorphs,  determiners,  inhibitors,  dominants  and  re- 
cessives,  genotyes  and  phenotyes,  are  anything  more  than 
ghosts,  without  substance ;  and  looking  always  for  simple 
explanations  of  a  physical  and  chemical  kind,  capable  of 

1  Bead  at  the  Symposium  on  Adaptation  at  the  meeting  of  the  American 
Society  of  Naturalists,  Cleveland,  January  2,  1913. 

90 


91  THE  AMERICAN  NATURALIST  [VOL.  XL VII 

expression  in  ordinary  language,  of  the  apparent  com- 
plexities of  evolution.  I  avow  myself  as  a  physiologist  to 
be  a  follower  of  Darwin,  admiring  his  methods  of  careful 
experiment  and  observation,  his  long  cogitations,  and 
with  confidence  in  the  soundness  of  his  judgment.  There 
has  been  a  tendency  of  recent  years  in  certain  quarters 
to  belittle  his  work,  to  make  fun  of  his  conclusions,  to 
deny  that  evolution  has  been  a  slow  and  steady  continu- 
ous process,  as  the  rocks  show,  and  to  assert  that  it  has 
taken  place  by  a  hop,  skip  and  a  jump,  and  that  it  would 
have  taken  place  anyway  without  natural  selection. 
Physics  and  chemistry  have  attempted  to  express  the 
physical  world  in  terms  of  matter  and  energy,  and  many 
biologists  are  attempting  to  extend  this  method  to  the 
living  world.  While  this  is  a  necessary  and  admirable 
thing  to  do,  it  must  not  be  forgotten  that  in  doing  so 
they  are  neglecting  the  main  fact  of  life,  consciousness, 
and  that  the  phenomena  of  life  can  not  be  accounted  for 
if  this  is  neglected.  It  is  obvious,  too,  that  the  physicist, 
with  his  present  conception  of  matter  and  energy,  is  mak- 
ing as  great  a  mistake  in  neglecting  the  psychical  side  of 
matter  as  the  biologist  would  make  if  he  neglected  the 
physical  side.  For  the  psychical,  like  the  physical,  must 
be  due  to  the  properties  of  the  atoms,  or  at  least  is  asso- 
ciated always  with  them.  For  the  atoms  are  the  same  in 
living  and  lifeless,  their  properties  are  inherent  in  them 
and  can  not  be  taken  away  and  added  to  them  as  if  they 
were  wagons,  which  changed  horses,  as  Du  Bois  Eay- 
mond  has  put  it. 

It  is  my  opinion  that  physiology  comes  powerfully  to 
the  support  of  Darwin's  conclusions ;  that  it  shows  clearly 
that  there  are  no  such  things  as  independently  variable, 
unit  characters ;  that  a  jump  is  a  physiological  impossi- 
bility; and  that  most  so-called  mutations  are  in  reality 
reversions,  as  Darwin  thought ;  and  in  this  position  physi- 
ology is,  I  believe,  supported  by  paleontology. 

But  while  accepting  many  of  Darwin's  conclusions,  we 
must  all  admit  that  many  phenomena  are  very  hard 


No.  554]        ADAPTATION  AND  THE  PHYSIOLOGIST  92 

to  understand  on  the  basis  of  Darwin's  explanations. 
Among  these  difficulties,  most  of  which  were  recognized 
by  Darwin,  there  are  the  phenomena  of  parallel  evolu- 
tion among  different  species  and  genera,  which,  though 
diverse,  appear  all  to  be  moving  forward  in  the  same 
direction;  the  phenomena  of  steady,  limited  progress  in 
one  direction  which  point  toward  orthogenetic  variation ; 
the  phenomena  of  the  appearance  of  rudiments  and  their 
development  until  useful.  It  is  exactly  these  difficulties 
upon  which  physiology  throws  some  light;  and  it  is  of 
them  that  I  particularly  wish  to  speak. 

In  the  evolution  of  animals  two  movements  may  be 
perceived :  a  spreading  out  and  a  progress ;  a  diversifica- 
tion and  a  movement  forward.  The  first  movement  is 
illustrated  by  the  formation  of  many  different  species 
in  one  genus;  or  of  many  genera  of  the  same  type  of 
animal ;  the  second  by  the  movement  forward  in  the  line 
of  evolution  of  all  these  species.  These  two  movements 
were  not  sharply  distinguished  by  Darwin,  but  they  have 
been  more  or  less  clearly  recognized  by  several  philoso- 
phers. It  is  this  double  movement  which  has  given  the 
animal  kingdom  the  form  of  a  branching  tree  instead  of 
a  single  trunk.  Darwin  dealt  mainly  with  the  first  of 
these  movements,  which  gives  rise  to  genera,  species  and 
varieties;  which  is  shown  by  the  diversification  of  ani- 
mals and  plants  in  domestication  by  human  selection; 
and  he  explained  it  by  the  progressively  better  adaptation 
of  forms  to  particular  environments.  He  believed  the 
second  movement,  the  movement  upward,  was  due  to  the 
same  cause. 

It  is  the  second  movement  which  has  been  so  hard  to 
explain  and  which  has  particularly  puzzled  the  paleon- 
tologist; the  successive  series  of  dominating  types  on 
the  earth's  surface  culminating  in  man;  the  progress 
steadily  toward  the  goal  of  consciousness  and  intelligence. 

The  question  which  I  wish  to  raise  is  whether  these  two 
movements,  which  are  at  right  angles  to  each  other,  may 
not  be  due  to  the  natural  selection  of  two  different  kinds 


93  THE  AMERICAN  NATURALIST          [VOL.  XL VII 

of  adaptations:  first,  adaptations  of  form  and  function  to 
different  kinds  of  environments ;  and  second,  the  natural 
selection  of  the  function  of  irritability,  or,  in  other  words, 
to  the  selection  of  adaptability,  or  the  adaptation  to 
changeableness  of  environment.  Selection  of  the  first 
kind  of  adaptations  may  have  given  rise  to  varieties, 
species,  genera  of  the  same  type  of  animal,  and  have  pro- 
duced the  spreading,  or  diversification ;  while  selection  of 
the  second  kind  of  adaptation  may  have  produced  the 
movement  onward  and  upward  of  all  animal  forms. 

These  two  kinds  of  adaptations  do  not  always  go 
together  and  selection  of  the  one  may  outweigh  the  other. 
It  is  because  selection  to  a  specific  environment  some- 
times is  more  important  than  selection  of  adaptations  to 
changeableness,  that  not  all  organisms  have  progressed 
in  the  scale  of  evolution  equally  rapidly:  but  some  have 
persisted  in  special  environments  with  slight  changes  of 
structure  for  very  long  periods,  or  may  even  have  retro- 
gressed; while  other  forms,  in  which  the  second  adapta- 
tion has  been  rigorously  selected,  have  moved  rapidly  on- 
ward and  upward,  and  show  little  adaptation  to  any 
special  environment. 

The  question  whether  evolutionary  progress  is  due  to 
the  selection  of  this  second  adaptation,  that  of  adapt- 
ability, occurs  very  naturally  to  a  physiologist,  because, 
in  the  first  place,  the  evolutionary  development  of  con- 
sciousness and  intelligence  appears  to  him  to  be  one  of 
the  most  important,  if  not  the  most  characteristic  move- 
ment in  evolution ;  and  in  the  second  place,  his  point  of 
view  in  considering  evolution  and  adaptation  is  some- 
what different  from  that  of  the  zoologist  or  the  paleontolo- 
gist. To  him  the  organism  does  not  appear  constituted 
of  bones,  skin,  horns,  or  other  structures,  but  to  be  consti- 
tuted essentially  of  a  number  of  mechanisms  in  activity, 
each  mechanism  having  a  definite  function  to  perform. 
Evolution,  for  the  physiologist,  is  not  evolution  of  struc- 
ture primarily,  but  evolution  of  function;  and  he  natu- 


No.  554]        ADAPTATION  AND  THE  PHYSIOLOGIST  94: 

rally  expects  to  find  that  the  adaptations  of  function  have 
been  of  great  importance  in  determining  survival. 

Of  all  the  physiological  properties  of  the  original  proto- 
plasm upon  which  natural  selection  might  be  supposed  to 
act,  irritability,  the  most  fundamental  property  of  living 
matter,  would  seem  the  most  probable  point  of  attack; 
for  irritability  is  that  property  of  protoplasm  in  virtue 
of  which  it  adjusts  itself  to  its  environment.  It  is  the 
property  of  response;  and  since  it  is  the  environment 
which  is  acting  as  the  judge  of  the  excellence  of  the 
response  and  doing  the  selecting,  it  would  seem  that  it 
must  be  upon  this  property  that  all  organisms  must  be 
tested.  It  is,  moreover,  this  property  that  Spencer  has 
very  acutely  selected  as  the  most  fundamental  charac- 
teristic of  living  organisms,  namely,  the  power  of  continu- 
ous adjustment  of  internal  to  external  conditions.  It 
would  seem  probable  that  however  well  animals  might  be 
adapted  to  special  environments  by  the  action  of  natural 
selection,  this  particular  property,  or  function,  which  has 
to"  do  with  the  continuous  adjustment  of  internal  to  ex- 
ternal relations  must  have  been  throughout  the  whole 
course  of  evolution  of  predominant  importance.  And  if 
there  has  been  any  unity  in  the  progress ;  if  the  course  of 
evolution  has  been  at  all  in  any  single  direction;  and  if 
the  natural  selection  theory  is  true;  it  must  be  in  the 
direction  of  the  perfecting  of  this  function. 

I  think  this  short  statement  will  make  it  clear  why  the 
physiologist  turns  naturally  to  this  fundamental  quality, 
or  property  of  living  things,  when  he  considers  evolution 
and  adaptation;  for  however  organisms  may  vary  in 
structure  or  other  particulars,  they  all  have  irritabilitv 
in  common.  Moreover,  I  think  most  physiologists  will 
agree  with  me  that  this  particular  property  has  been  too 
often  neglected  by  most  students  of  evolution,  amon^ 
whom  physiologists  have  been  unfortunately  very  rare. 

Irritability  shows  itself  in  all  cells  by  the  power  of 
internal  change  in  response  to  an  external  change.  In 
most  cells  of  the  body  there  is  nothing  especially  adaptive 


95  THE  AMERICAN  NATURALIST  [VOL.  XL VII 

in  the  nature  of  many  of  these  responses ;  but  it  is  quite 
otherwise,  if  we  consider  the  organisms  as  wholes.  It 
is  clear  that  all  organisms  have  not  only  the  power  of 
reacting  to  an  external  change,  but  many  of  their  reac- 
tions are  adaptive  to  a  surprising  degree.  This  is  indeed 
the  very  crux  of  the  difference  between  living  organisms 
and  lifeless  things.  A  lifeless  thing  can  not  adjust  its 
internal  to  its  external  relations  so  that  it  can  continue 
to  exist  in  a  changed  environment.  A  crystal  in  a  solu- 
tion of  its  kind  must  dissolve,  if  the  concentration  is  kept 
ever  so  little  below  saturation;  a  whole  universe  must 
pass  away,  if  anywhere  within  it  there  is  a  persistent 
uncompensated  difference  of  potential.  With  living  things 
it  is  quite  otherwise.  They  have  the  power  of  interposing 
resistances  to  the  potential  difference.  All  living  things 
without  exception  have  adaptive  responses  so  that  they 
are  able  to  continue  in  existence  even  though  their  sur- 
roundings change  in  many  different  ways.  They  possess 
adaptability.  Their  responses  due  to  their  irritability 
are  adaptive  responses.  The  irritability  of  the  organism 
as  a  whole  is,  then,  above  everything  else  characterized 
by  power  of  adaptive  response. 

It  is  not  difficult  to  imagine  how  this  specialization  of 
the  general  property  of  irritability  arose.  Some  of  the 
indefinite  responses  of  the  original  organisms  to  environ- 
mental change  protected  the  organism  against  the  change. 
Organisms  with  such  responses  survived  and  their  de- 
scendants had  the  property  of  a  limited  adaptive  response 
to  this  particular  change.  From  this  crude  beginning 
further  progress  was  easy.  The  changes  in  the  environ- 
ment, though  many,  are  not  indefinite  in  number,  and 
adaptations  in  the  nature  of  direct  responses  easily  arose 
and  were  perfected. 

Adaptability,  then,  appears  to  the  physiologist  as  the 
master  word  of  evolution.  And  many  facts  also  may  be 
urged  as  confirming  this  conclusion.  For  example,  one 
and  all  of  the  great  physiological  mechanisms  of  the  body 
have  a  single  purpose:  to  secure  adaptability.  Not  to 


No.  554]        ADAPTATION  AND  THE  PHYSIOLOGIST  96 

adapt  an  organism  to  one  environment,  but  to  all  environ- 
ments, and  thus  to  make  it  superior  to  all  environments. 
Furthermore,  the  higher  organisms  are  specially  remark- 
able for  the  development  of  that  master  tissue  of  the  body 
which  is  preeminently  irritable  and  of  which  the  main 
function  is  the  adjustment  of  internal  to  external  rela- 
tions, the  nervous  system ;  and  finally  that  the  inference 
is  sound  may  be  concluded  from  the  fact  that  it  is  by 
adaptability  and  by  no  other  quality  whatever  that  organ- 
isms may  be  arranged  in  the  order  of  their  evolutionary 
progress. 

It  is  not  at  all  surprising  that  adaptability  should  be 
the  most  important  adaptation  in  nature,  overpowering, 
except  in  special  cases,  and  dominating  all  others.  For 
there  is  but  one  certain  thing  in  nature:  namely  uncer- 
tainty. The  most  constant  feature  of  all  environments, 
but  particularly  of  land  environments,  has  been  their  in- 
constancy. Changeableness  is  the  chief  characteristic  of 
all  environments,  whatever  their  special  characters  may 
be.  There  are  changes  of  light,  temperature,  climate, 
oxygen  and  carbon  dioxide,  moisture;  changes  due  to 
the  introduction  of  new  species  by  migration  upsetting 
nature 's  balance ;  changes  in  the  food  supply.  Climates, 
flora  and  fauna  change;  change  alone  persists.  Change 
is  the  essential  thing.  We  may  expect,  therefore,  if 
Darwin  be  correct  in  his  conclusion  that  variation  and 
natural  selection  account  for  evolution,  that  adaptation 
to  changeableness  must  be  the  chief  adaptation  in  nature, 
and  more  than  all  others,  it  must  have  determined  the 
general  course  of  evolution.  This  is  found  to  be  the  case 
and  the  great  physiological  mechanisms  of  the  body  are 
designed,  as  already  stated,  to  subserve  this  fundamental 
adaptation.  Adaptability  is  that  power  which  fits  organ- 
isms to  withstand  the  unexpected :  the  vicissitudes  of  life ; 
special  adaptations  of  form  and  color  may  contribute  to 
the  survival  of  animals ;  but  the  essential,  or  root,  adapta- 
tion is  to  changeableness.  By  adaptation  to  all  environ- 
ments they  become  finally  superior  to  all  environments. 


97  THE  AMERICAN  NATURALIST  [VOL.  XL VII 

Superiority  to  environment,  and  not  adaptation  to  it,  is 
secured  through  the  irritability  of  the  organism  con- 
sidered as  a  whole. 

The  great  mechanisms  of  the  body  which  have  this 
function  are  several.  First,  the  heat-regulating  mechan- 
ism, for  by  means  of  this  organisms  are  rendered  inde- 
pendent of  the  temperature  of  their  environments.  They 
can  exist  in  the  tropics  or  in  the  arctics  and  withstand  the 
extremes  of  our  own  climate,  while  maintaining  their 
activities.  This  is  a  complex  mechanism  consisting  of 
insulating  material  in  the  skin;  trophic  nerves  to  the 
internal  organs;  a  closed  vascular  system;  a  power  of 
rapid  oxidation ;  supra-renal  capsules ;  pancreas ;  nervous 
coordination;  sweat  glands;  evaporation  of  water  in  the 
lungs;  temperature  nerves.  More  than  any  other  this 
mechanism  enabled  the  mammals  to  conquer  the  reptiles 
and  supplant  them.  The  mammals  became  independent 
of  the  temperature  of  their  environments.  A  mechanism 
not  coming  by  jumps,  but  the  rudiments  found  far  down 
in  the  fishes  and  slowly  evolved. 

A  second  fundamental  mechanism  of  great  importance 
for  the  mammals  in  supplanting  the  reptiles  and  other 
animals  probably  was  that  concerned  in  immunity.  Most 
of  the  toxins  of  poisonous  reptiles  are  of  a  protein  nature. 
The  mammals  have  developed  a  mechanism,  the  details 
of  which  are  still  obscure,  but  which  apparently  consists 
in  the  conversion  of  these  protein  toxins  into  bodies  which 
neutralize  the  toxins  from  which  they  are  formed,  that  is, 
into  antitoxins.  We  find,  as  a  matter  of  fact,  that  at  least 
many  of  the  mammals  are  able  apparently  to  make  an 
anti-toxin  out  of  any  kind  of  a  foreign  protein.  Besides 
this  mechanism  of  defense,  useful  against  bacteria,  as 
well  as  against  snakes,  there  is  the  primitive  mode  of 
phagocytosis  and  the  chemical  method  of  defense,  which 
consists  either  in  the  prevention  of  absorption,  or  in  the 
chemical  neutralization  of  the  poison  by  union  with  other 
substances.  Thus  the  toxicity  of  phenols,  benzoic  acid 
and  many  alkaloids  are  neutralized.  By  this  mechanism 


No.  554]        ADAPTATION  AND  THE  PHYSIOLOGIST  98 

mammals  are  rendered  superior  to  the  attacks  of  many  of 
their  enemies  and  to  this  extent  rendered  superior  to  their 
environments. 

Third,  there  is  the  mechanism  for  rendering  mammals 
tolerably  independent  of  the  moisture  content  of  their 
environment,  a  mechanism  most  highly  developed  in  the 
reptiles.  A  mechanism  formed  by  the  replacing  of  the 
wet  skin  of  the  amphibian  by  a  dry  or  scaly  skin;  the 
perfecting  of  the  kidneys  to  maintain  osmotic  pressure 
of  the  blood ;  the  control  of  the  sweat  glands  and  loss  of 
water  by  the  intestines;  the  development  of  membranes 
non-permeable  to  salts,  so  that  animals  may  sit  in  fresh 
water  and  not  lose  their  salts.  One  of  the  most  interest- 
ing parts  of  this  mechanism  is  shown  in  the  reptiles  and 
birds,  in  the  substitution  of  uric  acid  for  urea  in  their 
excretions.  By  this  improvement  reptiles  have  secured 
almost  complete  independence  of  the  water  content  of 
their  environments.  They  make  enough  water  in  their 
own  bodies  to  supply  their  small  losses.  This  again  is 
a  mechanism  of  which  we  can  trace  the  steady  growth 
without  a  break  from  the  invertebrates  to  man. 

A  fourth  great  mechanism  makes  mammals  independent 
of  barometric  fluctuations  and  less  dependent  on  a  fixed 
atmosphere.  By  means  of  their  blood  loaded  with  hemo- 
globin carried  in  corpuscles  lacking  all  oxygen- consuming 
power,  they  are  able  to  live  on  lofty  plateaus,  or  in  deep 
.valleys;  and  in  the  presence  of  much  or  little  carbon 
dioxide. 

The  mechanisms  having  to  do  with  reproduction  and 
the  caring  for  the  young  afterward  have  this  same 
advantage  of  rendering  the  mammals  independent  of 
environment. 

A  sixth  mechanism  is  the  alimentary  mechanism,  most 
highly  perfected  in  man.  This  has  rendered  him  inde- 
pendent of  any  particular  kind  of  food.  He  can  make 
his  body  of  any  kind  of  plant  or  animal.  He  can  make 
carbohydrate  out  of  protein  and  many  other  things.  He 
can  live  in  any  climate  largely  because  of  this  mechanism. 


99  THE  AMERICAN  NATURALIST  [VOL.  XL VII 

Again  a  complex  mechanism,  consisting  of  teeth,  of  diges- 
tive glands  tearing  proteins  and  carbohydrates  to  pieces, 
so  that  he  can  build  up  his  own  proteins  from  any  other 
kind,  useless  amino  acids  being  converted  into  sugar  and 
urea. 

The  last  and  by  far  the  most  important  of  these  great 
mechanisms  of  adaptability  is  that  which  provides  for 
every  contingency;  for  the  unexpected.  It  seems  that 
nature,  after  elaborating  these  other  mechanisms  to  meet 
particular  vicissitudes,  has  lumped  all  other  vicissitudes 
into  one  and  made  a  means  of  meeting  them  all.  One 
can  not  but  be  pleased  by  the  apparent  ingenuity  of  this 
solution.  I  refer  to  the  nervous  mechanism.  It  is  obvious 
how  this  mechanism,  by  substituting  choice  for  blind  in- 
stinct, consciousness  for  unconsciousness,  developing 
memory,  so  that  one  can  profit  by  experience,  and  intelli- 
gent adaptation  of  means  to  ends,  has  provided  finally  for 
all  possible  contingencies  of  the  future.  She  has  spoken 
her  last  word.  Adaptability,  or  superiority  to  environ- 
ment, was  the  end  so  blindly  sought ;  memory,  conscious- 
ness, choice  were  the  means,  shall  I  say  the  means  as 
blindly  adopted? 

To  the  physiologist,  then,  adaptability  appears  to  be 
the  touchstone  with  which  nature  has  tested  each  kind  of 
organism  evolved;  it  has  been  the  yard  stick,  with  which 
she  has  measured  each  animal  type;  it  has  been  the 
counterweight  against  which  she  has  balanced  each  of  her 
productions.  However  well  adapted  to  a  specific  environ- 
ment a  type  might  be,  did  it  lack  ever  so  little  of  its  possi- 
bilities in  this  direction,  it  was  sooner  or  later  relegated 
to  the  scrap  heap.  Some  forms,  to  be  sure,  persisted  in 
special  environments,  where  they  were  protected  from 
competition,  as  in  Australia;  or  where  the  environment 
was  fairly  constant,  as  in  the  sea;  or  in  special  environ- 
ments for  which  they  were  highly  suited;  but  the  whole 
trend  of  evolution,  with  these  exceptions,  may  be  summed 
up  by  the  statement :  the  general  course  of  evolution  has 
been  always  from  the  beginning  to  the  end,  in  the  direc- 


No.  554]        ADAPTATION  AND  THE  PHYSIOLOGIST  100 

tion  of  increasing  adaptability  or  increasing  perfection 
of  irritability.  This  law  may  be  put  by  the  side  of  the 
law  for  the  evolution  of  universes :  all  spontaneous  change 
is  in  the  direction  of  increasing  entropy. 

It  is  not  by  form,  by  color,  by  increasing  complexity  or 
simplicity,  that  animals  may  be  classified  in  the  order  of 
their  evolutionary  appearance.  It  is  by  this  property  of 
adaptability  and  this  alone.  At  the  summit  is  man ;  now 
consciously  attempting  to  carry  on  what  nature  has  been 
unconsciously  attempting  these  millions  of  years,  and  to 
secure  mastery  of  his  environment.  Below  him  are  the 
other  placenta!  mammals  of  lower  intelligence;  beneath 
them  the  marsupials,  less  adaptable  than  the  mammals, 
because  of  lower  brain  power ;  then  the  reptiles  independ- 
ent of  water,  but  not  of  temperature ;  the  amphibia,  only 
partially  independent  of  water,  but  not  of  temperature; 
the  teleosts  able  to  live  in  salt  and  fresh  water;  the 
selachians,  most  without  osmotic  control  and  limited  to 
the  sea ;  the  arthropods  living  on  land  and  sea,  but  depend- 
ent on  temperature,  food  and  climate,  cramped  by  an 
external  skeleton,  and  with  the  fatal  defect  of  running 
the  alimentary  canal  through  the  nervous  system,  so  that 
for  higher  brain  power,  either  a  new  nervous  system  or  a 
new  alimentary  canal  would  be  needed;  lower  still  the 
molluscs  and  annelids,  closely  limited  to  their  environ- 
ments ;  and  last  the  echinoderms  and  protozoa.  No  adap- 
tation or  power  of  the  body  has  been  so  consistently 
attacked  by  natural  selection  as  this ;  and  it  is  this  prop- 
erty which  seems  to  have  been  the  determining  factor  in 
the  general  course  of  evolution  and  to  have  determined 
the  steady  development  of  the  psychic  powers. 

I  come  now  to  the  second  part  of  my  subject,  namely, 
correlation.  By  the  first  part  I  have  attempted  to  show 
that  the  selection  of  variations  in  adaptability  is  respon- 
sible for  at  least  a  part  of  the  steady  progress  in  one 
direction  of  many  kinds  of  animals;  and  explains  that 
unity  of  progress  which  has  been  one  of  the  main  causes 
for  assuming  orthogenesis.  In  this  second  part  of  the 


101  THE  AMERICAN  NATURALIST          [VOL.  XL VII 

paper,  I  hope  to  show  that  the  development  of  our  knowl- 
edge of  correlation  removes  some  other  difficulties  which 
Darwin  had  to  meet,  and  probably  explains  some  other 
facts  which  have  been  urged  as  supporting  orthogenesis. 

Among  the  puzzles  of  evolution  has  been  the  steady 
growth  of  rudimentary  structures  which  have  apparently 
no  function  until  they  are  considerably  developed.  I  say 
apparently  no  function,  for  the  physiologist  has  learned 
to  be  very  cautious  in  saying  that  any  part  of  the  body 
is  without  function  or  use.  A  few  years  ago  it  was  quite 
otherwise  and  it  was  supposed  that  various  rudiments, 
like  the  appendix,  the  hypophysis,  the  pineal  gland,  the 
thymus  and  some  other  organs  were  without  function; 
the  surgeons  were  busy  explaining  how  much  better  we 
were  off  without  them ;  and  the  anti-Darwinian  was  fond 
of  presenting  these  things  as  not  consonant  with  the  view 
of  adaptation.  At  the  present  time  the  uselessness  of 
these  rudimentary  structures  is  no  longer  affirmed.  We 
must  therefore  be  very  cautious  in  supposing  that  any 
structure  we  see,  no  matter  how  insignificant  it  may 
appear,  is  without  importance.  Darwin  himself  felt  the 
great  fact  of  correlation,  and  his  pangene  theory  was 
invented,  in  part,  to  account  for  these  facts.  He  would 
be  both  astonished  and  delighted  could  he  know  how  com- 
pletely physiology  has  vindicated  his  appeal  to  correla- 
tion as  the  explanation  of  some  difficulties. 

Modern  physiology  has  shown  that  the  whole  animal 
organism  is  correlated  by  means  of  internal  secretions; 
that  there  is  but  one  unit  in  the  body,  and  that  is  the 
whole  organism.  By  the  work  of  Knowlton  and  Starling 
we  now  have  the  final  proof  of  the  correlation  of  the  pan- 
creas and  muscles.  The  correlations  between  the  hard 
and  soft  parts  of  the  body  are  of  still  greater  importance 
to  the  paleontologist,  for  it  has  been  shown  that  the  hard 
parts  are  not  independently  variable,  but  that  they  are 
dependent  at  every  point  upon  the  function  of  the  soft, 
internal  organs.  Who  would  have  dreamed  that  the  char- 
acter of  the  skin,  the  hair,  the  shape  of  the  skull,  the  in- 


No.  554]        ADAPTATION  AND  THE  PHYSIOLOGIST  102 

telligence  itself,  the  length  of  the  limbs,  or  the  speed  of 
transformation  of  a  tadpole  into  a  frog  would  be  depend- 
ent on  the  thyroid  or  thymus  gland?  That  the  minute 
parathyroids  should  be  absolutely  necessary  to  the  life  of 
an  organism  thousands  of  times  their  weight?  Or  that 
the  development  of  the  testes,  the  change  of  milk  teeth 
to  the  permanent  dentition,  the  growth  of  the  bones  of 
the  extremities,  should  be  dependent  on  the  anterior  lobe 
of  that  apparently  useless  rudiment,  the  hypophysis?  Or 
that  the  secretion  of  milk  and  urine  should  depend  on  the 
posterior  lobe  of  the  same  organ?  Who  had  the  temerity 
to  suggest  that  the  corpus  luteum  should  be  influencing 
the  development  of  the  mammary  glands  ?  Do  we  not  see, 
indeed,  that  most  of  the  characters  of  the  body  which 
have  steadily  developed  from  the  fishes  to  man  are 
secondary  characters  dependent  on  the  anterior  develop- 
ment of  these  ductless  glands?  Is  this  fact  without  sig- 
nificance to  the  paleontologist  in  helping  him  to  under- 
stand the  apparent  steady  progress  in  one  direction,  the 
appearance  of  orthogenesis?  It  will  be  asked,  perhaps, 
what  has  caused  the  steady  development  of  these  glands. 
But  the  answer  is  not  difficult.  They  are,  in  their  turn, 
parts  of  the  mechanism  of  adaptability  which  has  been 
consistently  selected  in  evolution.  They  are  concerned 
not  only  in  the  growth  of  bone,  but  in  the  growth  of  the 
nervous  system,  the  heat  control  of  the  body,  the  im- 
munity mechanisms,  the  efficiency  of  muscles,  and  are  in 
the  chain  of  reproduction  itself.  These  facts  largely 
remove,  in  my  opinion,  the  difficulties  in  understanding 
how  rudimentary  organs  could  be  useful. 

But  not  only  do  these  facts  remove  these  difficulties  in 
the  way  of  the  selection  theory,  but  they  have  a  no  less 
important  bearing  on  the  problem  of  heredity.  They 
show  that  there  can  be  no  independently  variable  quali- 
ties in  the  animal  body.  The  body  is  a  unit,  and  I,  at 
least,  can  imagine  no  part  of  it  which  can  vary  without 
influencing  other  parts.  Correlations  are  everywhere. 
Pigment  is  often  cited  as  a  unit  character,  but  how  can  it 


103  THE  AMERICAN  NATURALIST  [VOL.  XLVII 

be  so  1  Pigment  is  itself  the  result  of  a  long  and  complex 
series  of  changes.  If  a  given  cell  produces  no  pigment  it 
is  perfectly  certain  that  its  other  chemical  processes 
are  to  some  degree  modified  also,  so  that  these  other 
things  vary  also.  If  this  cell  is  changed  so  that  it  pro- 
duces no  pigment,  then  since  it  is  the  logical  result  of  a 
long  series  of  changes  in  the  developing  organism,  those 
changes  must  have  been  different  in  animals  producing 
pigment  and  no  pigment.  But  this  means,  since  each 
process  in  the  early  stage  of  development  influences  a 
multitude  of  processes  in  the  final  change,  that  there  must 
be  a  host  of  differences  correlated  with  the  pigment 
change.  As  a  matter  of  fact,  Darwin  long  ago  pointed  out 
that  pigment  production  was  apparently  correlated  with 
other  factors;  particularly  with  vital  resistance,  a  fact 
repeatedly  mentioned  to  the  writer,  also  by  Whitman  as 
a  result  of  his  experiments  in  pigeon  breeding.  Darwin 
cites  the  case  of  the  Virginia  pigs  of  which  only  the  black 
ones  could  eat  a  poisonous  root  without  losing  their  hoofs ; 
and  Whitman  told  me  that  always  birds  deficient  in  pig- 
ment were  also  somewhat  deficient  in  other  characters 
and  were  weaker. 

The  essential  unity  of  the  organism  is  not  only  fatal  to 
the  whole  theory  of  unit  characters,  but  it  is  an  insuper- 
able objection  to  the  theory  that  evolution  has  been  by 
jumps.  The  organism  is  a  finely  adjusted  mechanism  of 
a  very  complex  kind ;  it  seems  impossible  to  a  physiolo- 
gist that  one  can  cause  a  sudden  large  change  in  any  part 
of  it  and  have  it  continue  to  function ;  it  is  as  incredible 
as  if  one  should  remove  one  of  the  wheels  of  a  watch, 
replace  it  by  a  larger  one,  and  expect  the  watch  to  con- 
tinue to  run.  Such  a  simple  matter  as  the  replacement 
of  urea  by  uric  acid  as  an  excretion,  a  change  which  the 
reptiles  introduced  in  their  differentiation  from  the  am- 
phibia, a  change  which  might  conceivably  be  brought 
about  by  the  dropping  out  of  a  uricolytic  enzyme,  could 
not  take  place  suddenly.  The  kidneys  and  all  other  organs 
of  the  body  would  need  to  be  adjusted  to  this  change. 


No.  554]        ADAPTATION  AND  THE  PHYSIOLOGIST  104 

Finally  correlation  has  greatly  enhanced  the  value  of 
the  old  idea  of  checks  in  development  and  shows  most 
clearly  that  no  organ  of  the  body  ever  reaches  its  full 
potentialities.  What  comes  out  of  an  egg  is  but  one  of 
the  infinite  potentialities  contained  in  it.  Velocity  of  de- 
velopment, like  every  other  chemical  reaction,  is  equal  to 
the  affinity  divided  by  the  resistance.  If  resistances  are 
increased,  or  if  vitality,  in  other  words  chemical  affinity, 
be  reduced,  the  development  must  stop  sooner  than 
normal;  and  we  have  the  phenomena  of  reversion.  If, 
on  the  other  hand,  the  reverse  takes  place,  if  vitality  is 
increased  or  resistance  reduced,  we  have  variation  in  the 
direction  of  evolution.  The  development  of  nonviable 
monsters  is  at  one  extreme  of  this  process.  Ontogeny  is 
like  a  runner,  taking  the  first  hurdles  easily,  but  always 
with  increasing  difficulty,  sometimes  trippling  at  one, 
sometimes  at  another,  but  never  reaching  the  end  of  his 
race. 

In  conclusion  then:  to  the  physiologist  it  appears  that 
the  best  explanation  of  adaptation  is  that  given  by  Dar- 
win of  natural  selection  of  small  variations;  that  the 
essential  unity  of  the  progress  in  evolution  toward  con- 
sciousness and  intelligence  has  been  due  to  the  natural 
selection  of  the  fundamental  property  of  irritability,  for 
it  is  in  virtue  of  this  property  that  adaptability  of  organ- 
isms has  been  increased.  The  recognition  of  this  fact  re- 
moves one  of  the  difficulties  in  the  way  of  Darwin's  the- 
ory. And,  second,  physiology  by  the  establishment  of  the 
physiological  correlation  of  all  parts  of  the  body,  hard 
and  soft,  interposes  a  final  objection,  in  my  opinion,  to 
the  whole  theory  of  unit  characters,  of  independent  vari- 
ability of  characters,  and  to  the  theory  of  evolution  in 
any  other  way  than  by  a  slow  and  gradual  process,  which 
shall  give  time  to  the  readjustments  of  every  part  of  the 
body  necessitated  by  a  change,  however  slight,  in  any 
part  of  it. 


A    METHOD    OF   DETERMINING    "a"    OF    VAN    DER 
WAALvS'  EQUATION  FROM  THE  SUR- 
FACE TENSION 


BY    ALBERT   P.    MATHEWS. 

Uncertainty  still  exists  as  to  the  correct  value  of  van  der 
Waals'  constant  "a,  "  which  expresses  the  cohesive  pressure  of 
a  fluid. 

It  is  well  known  that  if  "a"  and  "6"  are  both  supposed 
to  be  constant,  the  equation  of  state  may  be  solved  and  the 
relationships  obtained:  a  =  3PCVC2;  Vc  --=  36;  Pc  ==  a/2~b2;  and 
T,  =  8a/2jbR.  As  this  solution  depends  on  the  er- 
roneous assumption  of  the  constancy  of  ''6,"  there  is  no 
certainty  that  any  of  these  expressions  is  correct;  and  as  a 
matter  of  fact,  only  one  of  them,  i.  e.,Pc  =  a/2jb2,  happens 
to  approximate  very  closely  to  a  correct  value.  Were  these 
relationships  true,  the  calculation  of  "a"  and  "6"  from  the 
critical  data  would  be  very  simple;  but  as  they  are  not  true, 
except  for.  unknown  values  of  "6,"  ii:  is  necessary  to  find 
some  other  means  of  computing  "a,"  which  does  not  require 
a  knowledge  of  the  real  molecular  volume,  or  "  b. " 

While  the  formula  usually  employed  for  the  calculation 
of  "a,  '  ;.  r.,  a  =  271^/64  X  273"  X  Pc,  gives  a  value  at  least 
approximately  correct  for  non-associating  substances  of  me- 
dium molecular  complexity,  it  is  still  uncertain  whether  the 
value  thus  obtained  is  correct  for  very  simple  substances 
such  as  hydrogen,  or  for  very  complex  substances  such  as 
diphenyl  methane.  The  ratio  27/64  can  only  be  justified 
theoretically  if  "6"  were  constant  and  it  is  probable  that 
this  ratio,  27/64,  is  not  constant,  but  diminishes  as  molecular 
compressibility  increases.  "6C"  may  not  always  be  the 
same  fraction  of  V c,  for  it  is  possible  that  this  fraction  also 
varies  with  the  compressibility  of  the  molecule.  All  other 
formulas  for  "a"  are  also  more  or  less  unsatisfactory.  Thus 
in  the  formula  a  --=  6.28VC2PC,  the  coefficient  is  not  the  same 
for  all  substances.  In  the  formula  a  --=  2jbc2Pc  a  knowledge 


Determining  "a"  of  van  der  Waals'  Equation  155 

of  bc  is  required.  The  calculation  of  "a"  from  the  latent 
heat  of  vapor/i&on  by  the  formula  (L  -  -  E)/^  -  -  DJ 
a/Mol.wt,  where  L  is  the  total  latent  heat  and  E  the  part 
consumed  in  doing  external  work,  is  rendered  uncertain  by 
the  fact  that  there  is  still  another  part  of  the  heat  consumed 
by  the  expansion  of  the  molecules  from  the  size  they  are  in 
the  liquid  to  the  size  they  are  in  the  vapor,  and  this  correc- 
tion is  unknown. 

The  following  method  of  the  comffumption  of  "a"  from 
the  surface  tension  is  new,  so  far  as  I  can  find,  although  it  is 
an  application  of  the  very  first  method  used  to  obtain  some 
idea  of  the  amount  of  the  cohesive  pressure  of  a  liquid;  it 
does  not  involve  the  value  "6;"  and  it  is  of  interest  that  the 
results  obtained  from  it  are,  on  the  whole,  closely  similar  to 
those  given  by  the  usual  formula.  It  is,  I  believe,  more 
trustworthy  than  the  formula  usually  employed.  It  is  a 
method  proposed  by  the  great  English  philosopher,  Thomas 
Young,  in  his  epoch-making  work  on  Cohesion.  In  that 
work,  by  an  insight  little  short  of  marvelous,  he  came  to  the 
conclusion  that  S,  the  surface  tension,  was  equated  to  one- 
third  the  total  cohesive  pressure,  multiplied  into  the  radius 
of  action  of  the  cohesive  attraction,  or  S  ==  rK/$. 

Since  "a"  varies  with  the  volume  of  the  gas  taken  under 
standard  conditions  of  temperature  and  pressure,  it  would  be, 
in  many  ways,  convenient  to  have  a  value  which  was  character- 
istic of  the  molecules  of  each  substance  and  which  would  be 
independent  of  the  volume  of  gas  or  liquid,  or  the  tempera- 
ture ©f- pressure  to  which  it  was  subjected.  Such  a  value  is 
very  easily  obtained  by  putting  "a"  equal  to  N2M2K,  where 
N  is  the  number  of  molecules  in  the  volume  V;  and  writing 
V2  as  NiT3;  where  small  v  is  the  volume  at  the  disposal  of  a 
single  molecule.  By  dividing  by  N2  we  have  then  a/V2  = 
M2K/i>2.  We  may  call  M  the  mass  of  cohesion  of  a  molecule, 
and  K  is  a  constant  of  proportion.  This  same  value  may  be 
obtained  directly  by  supposing  that  molecules  attract  each 
other  inversely  as  the  fourth  power  of  the  distance  between 
their  centers,  directly  as  the  product  of  their  cohesive  masses 


156  Albert  P.  Mathews 

and  that  each  molecule  attracts  only  the  six  surrounding 
molecules.  In  another  paper  I  shall  show  that  the  value 
M2K  is  proportional  to  the  two- thirds  power  of  the  product 
of  the  molecular  weight  and  the  number  of  valences  in  the 
molecule.  In  this  paper  I  wish  to  show  how  M2K  may  be 
derived  from  the  surface  tension.  The  computations  are 
made  in  absolute  units. 

The  formula,  S  ==  fK/3,  states  that  the  surface  tension 
of  a  liquid  is  a  function  of  the  cohesive  pressure  of  the  liquid 
alone.  It  is  clear,  then,  that  this  formula  can  hold  only  at 
very  low  temperatures,  since  only  at  such  temperatures  can 
the  cohesive  pressure  in  the  vapor  be  neglected.  The  surface 
tension,  strictly  speaking,  can  not  represent  the  cohesive 
pressure  of  the  liquid  alone,  since  it  is  in  the  very  nature  of 
things  an  expression  of  the  difference  in  cohesive  energy  of 
the  liquid  and  vapor.  I  shall,  then,  take  the  formula  as 
holding  at  absolute  zero,  since,  if  we  are  going  to  a  tempera- 
ture in  which  the  vapor  may  be  entirely  neglected,  it  is  more 
convenient  to  go  to  the  end. 

The  radius  of  action  of  the  cohesive  attraction,  or  r,  has 
been  found,  both  by  calculation  and  by  direct  measurement, 
to  be,  at  higher  temperatures,  very  nearly  equal  to  the 
distance  between  the  molecular  centers;  and  at  absolute  zero, 
with  the  molecules  in  contact,  we  may  safely  assume  that 
"r"  is  equal  to  vl/'\  K  is  Laplace's  constant  and  is  equal  to 
a/V2,  or  M2K/i;2.  The  formula  becomes  then:  S  = 
DQ  1/3M2K/>0  2  =  M2K/3i;0 5/3.  By  multiplying  both  sides  of  the 
equation  by  v02/3  we  have,  $v0 2/3  ==  M2K/3?;0  ;  v0,  the  volume 
at  the  disposal  of  one  molecule  at  absolute  zero,  is,  for  sub- 
stances of  medium  complexity  such  as  ether,  very  nearly 
equal  to  TJC,  the  volume  of  a  molecule  at  the  critical  tempera- 
ture, divided  by  4.  For  simpler  substances,  such  as  O2  or 
CO2,  the  volume  v0  is  equal  to  Vc/3.63;  and  for  more  complex 
substances,  such  as  octane,  it  is  1^/4.04,  or  for  some  even 
i;c/4.io.  The  volume  of  a  molecule  is  obtained  by  dividing 
the  volume  of  a  gram  mol  by  6.21  X  io23,  which  is  the  most 
probable  number  of  molecules  in  a  gram  mol.  There  is  a 


Determining  "a"  of  van  der  Waals'  Equation        157 

difference  of  opinion  as  to  the  value  of  the  coefficient  which 
is  given  as  1/3  by  Young,1  but  as  3/20  by  Rayleigh.2  As 
will  be  shown  presently,  Young's  value  is  to  be  preferred. 

The  value  of  Si^02/3,  the  molecular  surface  tension  energy 
at  absolute  zero,  may  be  obtained  from  Eotvos3  and  Ramsay 
and  Shields'4  rule,  $(m<v)213  -=  2.12  (or  2.ig)(Tc  —  T  —  6). 
S(w7;)2/3  divided  by  N2/3,  where  N  is  the  number  of  molecules 
in  one  gram  mol,  equals  Si;2/3.  Hence  S^2'3 
2.i9(Tc  —  -  T  -  -  6)/N2/3;  and  at  absolute  zero,  where  T  is 
zero,  S<z;02/3  =  2.i9(Tc  —  6)/N2/3  ==  3.015  X  io-16(Tc  — 6)  ergs. 
It  is  assumed  that  the  law  holds  clear  to  absolute  zero. 

I  have  used  the  coefficient  2.19  because  I  thought  it 
more  typical  of  a  non-associating  substance,  and  it  is  nearer 
to  the  value  of  Eotvos.  However,  this  has  given  me  slightly 
higher  values  for  "a"  than  those  generally  computed,  as  may 
be  seen  in  the  table.  The  agreement  with  other  values  of 
"a"  seemed  on  the  whole  better  with  this  coefficient.  It 
varies  slightly  with  different  substances  in  any  case  being 
nearly  2,  for-  some  gases  like  oxygen,  and  as  high  as  2.3  for 
very  complex  substances.  2.19  comes  close  to  the  mean. 

We  have  then  $V/3  -  M2K/3^0  =  3.015  X  iQ-16(T  -  -  6) 
ergs.  SoM2K  -=  9.045  X  iQ-16(Tc  —  6)v0. 

The  value  6°  subtracted  from  the  critical  temperature 
was  established  for  substances  having  a  critical  temperature  of 
about  4oo°-48o°  Abs.  It  would  be  better  perhaps  to  make 
it  i/8oth  of  Tc.  The  formula  corrected  thus  would  be  M2K  = 
9.045  X  io~16Tci;0 79/80  =8.932  X  io-16TcT;0.  As  this  last 
correction  is  uncertain,  however,  I  have  uniformly  subtracted 
6°  from  the  critical  temperature,  unless  it  is  specifically 
stated  to  the  contrary. 


1  Young:  "An  Essay  on  the  Cohesion  of  Fluids,"  Philosophical  Trans- 
actions, 1805.     (Collected  works,  edited  by  G.  Peacock,  Vol.  I,  1855,  p.  418, 
London.) 

2  Rayleigh:  Article     on     "Capillarity,"     Encyclopoedia    Britannica,     xi 
edition. 

3  Eotvos:  Wied.  Ann.,  27,  458  (1886). 

4  Ramsay  and  Shields:  Zeit.  phys.  Chcm.,  12,  433  (1893). 


158  Albert  P.  Mathews 

As  already  mentioned  there  is  an  uncertainty  whether 
the  coefficient  should  be  //3,  as  found  by  Young,  or  3/20,  as 
found  by  Rayleigh.  As  I  was  unable  to  decide  which  of  the 
values  of  the  coefficient  was  preferable,  I  tried  them  both, 
and  Young's  value  gives  a  consistent  result.  Rayleigh 's 
gives  an  impossible  result,  the  cohesive  pressure  computed 
by  it  being  more  than  double  what  it  ought  to  be,  so  that 
if  it  be  substituted  in  van  der  Waals'  equation,  bc  must  be 
taken  very  large  and  at  what  are  impossible  values.  For 
example,  b  c  must  be  o.748Vc,  or  nearly  three-fourths  of  the 
critical  volume,  if  the  coefficient  3/20  is  used.  Such  a  value 
for  "b"  is  impossible  if  the  atoms  retain  their  uniform  size  in 
the  molecules,  or  if  they  change  very  little,  since  the  intra- 
molecular cohesion  is  so  much  greater  than  the  intermolecular 
that  the  greater  part  of  the  gain  in  volume  in  coming  from 
zero  to  the  critical  temperature  must  be  in  the  spaces  between 
the  molecules,  rather  than  within  them.  If  the  atoms  are 
incompressible  and  make  up  one-fourth  of  the  total  volume, 
then  three-fourths  of  the  critical  volume  will  be  free  space. 
If  bc  =  o.75Vc  and  the  atomic  volume  is  o.2$Vc,  then  free 
space  within  the  molecule  will  be  o.  5\rc,  leaving  only  a  total 
of  o.25Vc  for  the  inter-molecular  space.  In  other  words,  the 
space  within  the  molecules  would  have  enlarged  more  in  pass- 
ing from  zero  to  the  critical  temperature  than  the  space  be- 
tween the  molecules.  Such  a  result  is  impossible.  With 
Young's  formula,  however,  bc  ==  o.5Vc  approximately;  if  the 
atomic  volume  is  o.2^Vc,  then  the  free  space  within  the  mole- 
cules would  be  o.25Vc  and  between  the  molecules,  o.5Vc, 
which  is  a  more  probable  result. 

The  following  values  of  M2K  were  obtained  by  the  for- 
mula, M2K  =  vc  X  9-045  X  io~16(Tc  -  -  6)/4: 


Substance 


log10M'K 


Pentane 


—35-7I9I9 


Isopentane  — 35 . 70663 

Methyl  acetate  —35  .61791 

Ether  -35-67593 


Determining  "a"  of  van  der  Waals'  Equation        159 


With  the  values  thus  found  for  four  of  the  most  carefully 
investigated  non-associating  substances,  the  value  of  the  real 
molecular  volume,  or  bc,  at  the  critical  temperature  was  com- 
puted by  substituting  in  van  der  Waals'  equation,  with  the 
following  result : 


Substance 

vc 

bc 

Vclbc 

Ether 
Pentane 
Methyl  acetate 
Isopentane 

282.23 
309.94 
227-55 
307.30 

I35-8I 
149.44 
109.09 
148.30 

2.078 
2.074 
2.086 

2  .072 

By  substituting  the  values  of  M2K  derived  in  the  fore- 
going manner  from  the  surface  tension,  bc  turns  out  to  be  the 
same  fraction  of  Vc  for  the  three  best  investigated,  normal 
substances,  ether,  pentane  and  iso-pentane,  a  result  antici- 
pated from  van  der  Waals'  reduced,  characteristic  equation. 
Vc  is,  therefore,  2.074^.  The  value  thus  obtained  for  bc, 
namely  V  72.074,  is  very  close  to  that  calculated  by  van 
der  Waals  from  a  value  of  "a"  obtained  from  the  coefficient 
of  compressibility.  He  thus  obtained  the  value  Vc  ==  2.036^ 
Other  estimates  of  bc  made  by  him  bring  it  about  2.08.  This 
value  of  bc,  moreover,  is  inherently  probable,  the  value  of  bc 
necessarily  being  close  to  Vc/2,  and  presumably  a  little  less 
than  this. 

We  may  now,  with  this  value  of  bc  fixed,  calculate  by 
substitution  in  van  der  Waals'  equation  the  value  of  the 
coefficients  in  the  formulas  given  on  page  154  in  place  of  those 
derived  when  "a"  and  "b"  were  considered  constant. 

The  following  relationships  were  obtained  :2 

1  a/Pc  =  6.284V,2;  in  place  of  a/Pc  =  3VC2. 

2  V^  =  2.074^;  in  place  of  Vc  =  $bc. 

3  pc  =  a/27.026c2;  in  place  of  Pc  =  a/2jbc2. 

4  Tc  ==  7.769a/27.02R6c;  in  place  of  Tc  =  8a/2jRbc. 


5  bc  +  RTC/PC  =  4-243  Vc;  in  place  of  bc  +  RTC/PC  =  3VC. 

6  PCVC/TC  ==  R2.074/7.769  =  21.92;  in  place  of  PCVC/TC  -  3R/8  * 

30.80. 

7  RTC/PCVC  =  3-75- 

1  Van  der  Waals:  Proc.  Roy.  Acad.  Sci.,  Amsterdam,  3,  583  (1901). 

2  Compare  with  van  der  Waals:  Proc.  Roy.  Acad.  Sci.,  Amsterdam,  13, 
(1912). 


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Determining  "a"  of  van  der  Waals'  Equation       161 

The  value  of  21.92  thus  obtained  for  PCVC/TC  corresponds 
with  the  value  determined  from  Young's  very  careful  obser- 
vations on  the  critical  data  of  some  non-associating  substances. 

The  values  obtained  for  M2K  by  the  use  of  the  foregoing 
formulas,  the  surface  tension  formula,  and  the  ordinary  for- 
mula, when  applied  to  the  critical  data  of  the  substances  so 
carefully  investigated  by  Young1  are  given  in  Table  I. 

The  value  of  "a"  in  atmospheres  for  i  cc  of  a  gas  under 
standard  conditions  of  pressure  and  temperature  may  be 
obtained  from  any  of  the  values  in  this  table  by  multiplying 
by  7-573  X  io32. 

A  comparison  of  columns  3  and  4  of  Table  I  will  show 
that  the  values  obtained  by  the  surface  tension  formula,  while 
on  the  whole  closely  similar  to  those  obtained  by  the  ordinary 
formula  given  in  column  4,  differ,  nevertheless,  in  some  in- 
stances quite  markedly  from  them.  The  values  of  column  3, 
on  the  other  hand,  are  almost  identical  with  those  of  column 
i.  Owing  to  the  fact  that  there  is  less  uncertainty  about  the 
factors  used  in  computing  "a"  from  the  surface  tension  than 
from  the  usual  formula,  I  believe  the  surface  tension  values 
are  to  be  preferred.  If  the  coefficient  in  the  surface  tension 
formula  had  been  taken  as  2.12  instead  of  2.19,  all  the  values 
of  column  3  would  need  to  be  reduced  proportionally,  and  the 
values  in  columns  i  and  2  would  also  be  lower.  That  the  values 
of  "a"  computed  in  this  way  from  the  surface  tension  are  the 
more  accurate  is  indicated  also  by  the  fact  that  these  values 
exhibit  most  clearly  and  with  fewest  exceptions  the  relation 
of  cohesion  to  molecular  weight  and  the  number  of  valences 
in  the  molecule,  as  is  set  forth  in  a  subsequent  paper.  • 

University  of  Chicago 


1  Young:  "The  Vapor  Pressures,  Specific  Volumes,  Heats  of  Vaporiza- 
tion and  Critical  Constants  of  30  Pure  Substances,"  Proc.  Roy.  Dublin  Soc., 
12,  374-443  (1910). 


THE  RELATION  OF  THE  VALUE  "a"  OF  VAN  DER 

WAALS'  EQUATION  TO  THE  MOLECULAR 

WEIGHT  AND  THE  NUMBER  OF 

VALENCES  OF  THE 

MOLECULE 


BY  ALBERT  p.  MATHEWS 

The  discovery  of  the  properties  of  the  molecule  upon 
which  cohesion  depends  is  a  matter  of  great  interest.  I  have 
found  that  "a"  of  van  der  Waals'  equation  is  equal  to  a  con- 
stant multiplied  into  the  square  of  the  cube  root  of  the  product 
of  the  molecular  weight  by  the  number  of  valences  in  the 
molecule.  This  enables  a  calculation  of  the  valence  number 
of  a  molecule  from  the  critical  constants;  and  on  the  other 
hand  a  calculation  of  "a"  from  the  valence  and  molecular 
weight.  Some  interesting  facts  have  been  discovered  rela- 
tive to  the  valence  of  the  halogens,  of  the  argon  group  and 
some  other  elements  by  the  application  of  this  rule. 

If  the  value  a/V2  of  van  der  Waals'  equation,  which  repre- 
sents the  internal,  or  cohesive,  pressure  per  unit  surface, 
be  divided  in  both  the  numerator  and  denominator  by  N2, 
N  being  the  number  of  molecules  in  the  volume  V,  we  obtain  a 
value  for  "a  "  .which  may  be  called  the  molecular  cohesive  pres- 
sure and  which  is  independent  of  the  volume.  If  "  a  "  be  repre- 
sented by  the  expression  N2M2K,  in  which  M  is  the  mass  of 
cohesion  of  a  molecule  and  K  a  constant,  then  since  V2  is 
equal  to  N  V,  v  being  the  volume  at  the  disposal  of  a  single 
molecule,  a/V2  ==  N2M2K/NV  ==  M2K/V.  This  value  M2K 
may  be  computed  from  "a"  by  dividing  the  latter  by  N2. 
N,  the  number  of  molecules  in  a  cc.  of  gas  under  standard 
conditions,  is  equal  to  2.77  X  io19.  In  the  computations 
which  follow  I  have  taken  the  value  of  "a"  in  dynes  instead 
of  atmospheres  and  wherever  possible  I  have  used  the  value 
of  M2K  computed  by  the  surface  tension  formula  described 
in  a  previous  paper.1 


1  Mathews:  Jour.  Phys.  Chem.,  17,  154  (1913). 


182 


Albert  P.  Mathews 


Tables  I  and  II  bring  out  the  relationship  that  M  is  some 
function  of  the  molecular  weight  and  the  number  of  valences 
in  the  molecule,  or  M2K  ==  /  ,(Wt)  (Valence) .  The  relationship 
to  molecular  weight  appears  if  we  compare  compounds  of 
the  same  valence  number  as  shown  in  Table  I. 

TABLE  I 


Substance 

Mol.  weight 

Valences 

M2K  X  io:{5 

CO.,                                                 44  .  0 

8 

I  .216 

CC14 

153-8 

8' 

5-526 

GeCl, 

214-3 

8 

6.274 

SnCl4 

260.8 

8 

7-499 

C6H6 

78.0 

30 

5.181 

C6H5F1 

96.0 

30 

5-465 

C6H5C1                                  112.45 

30 

7.017 

C6H5Br 

157-0 

30 

7.8io(?) 

C6H5I 

204.0 

30 

9-i35(?) 

Ether                                       74.0 

28 

4-797 

Methyl  propionate                88  .  o 

28 

5-377 

Ethyl  acetate                         88  .  o 

28 

5-397 

It  is  clear  from  Table  I  that  the  factor  M2K  increases 
steadily  with  the  molecular  weight. 

The  importance  of  valence  is  shown  in  Table  II.  A  heavier 
compound,  if  it  have  fewer  valences,  may  have  a  lower  mass 
of  cohesion  than  a  lighter  substance. 

TABLE  II 


Substance 

Mol.  weight 

Valences 

M'K  X  io''5 

C8H5I 

SnCl4 

204.0 
260.8 

30 

8 

9-135 
7-499 

C6H5Br 
CC14 

157-0 
153-8 

30 

8 

7.810 
5-526 

Iso-pentane 
Ether 
Ethyl  formate 

72.0 
74-o 
74.0 

32 

28 

22 

"      5-089 

4-797 
4.  1  88 

1  The  valence  of  the  halogens  in  this  and  the  next  table  is,  for  simplicity, 
taken  as  unity.     Their  true  valence  is  discussed  farther  on. 


Value  of  "a"  of  van  der  Waals'  Equation  183 

It  might  also  be  imagined  that  the  mass  of  cohesion  was 
a  function  of  the  number  of  atoms  in  the  molecule,  rather 
than  the  number  of  valences,  but  a  trial  of  this  possibility 
showed  that  this  was  not  the  case. 

After  many  trials  in  which  the  mass  of  cohesion,  or  the 
factor  M2K,  was  supposed  to  be  a  function  of  the  first  power, 
the  square,  the  square  root,  or  the  square  of  the  cube  root  of 
the  product  of  the  number  of  valences  and  the  molecular 
weight,  it  was  found  that  only  the  last  supposition  yielded  a 
consistent  result.  In  all  the  other  guesses,  the  proportion- 
ality factor  "  C  "  was  far  from  being  constant.  Hence  we  have : 
M2K  -*  C(Wt  X  Val.)*'*. 

With  the  values  of  M2K  computed  by  the  surface  tension 
formula  it  was  found  that  the  quotient  M2K/(Wt.  X  Val.)2/3 
was  indeed  as  constant  as  could  be  expected  and  C  had  a  mean 
value  of  2  .98  X  io~37,  when  M2K  is  the  square  of  the  mass  of 
cohesion  of  one  molecule  multiplied  by  K  and  expressed  in 
absolute  units.  If  "a"  of  van  der  Waals'  equation  is  taken 
for  i  cc.  of  gas  under  standard  conditions  and  expressed  in 
atmospheres,  the  proportionality  factor  C  would  be  2  .  2564  X 
io~4.  This  gives  values  for  "a"  a  little  higher  than  those 
generally  accepted  owing  to  my  having  used  the  coefficient 
2.19  instead  of  2.12  in  computing  M2K  from  the  surface 
tension.  The  computation  of  "a"  for  ether  by  the  formula 
2.2564  X  io~4  (Weight  X  Valences) 2/3  gives  the  value 
0.03669,  whereas  the  value  from  the  usual  formula  of  van  der 
Waals  is  0.03473;  the  coefficient  2.12  would  have  given  the 
value  0.03550.  The  fact  that  these  values  are  throughout 
proportionally  somewhat  higher  than  those  usually  assumed 
does  not  affect  the  constancy  of  C. 

Table  III  shows  that  the  quotient  M2K/(Wt.  Val.)*'1  really 
equals  a  constant  when  M2K  is  computed  for  the  compounds 
of  carbon,  hydrogen  and  oxygen  of  which  the  critical  data 
have  been  so  carefully  determined  by  Young.  For  the  ele- 
ments of  these  compounds  there  is  no  doubt  of  the  valence 
number.  Carbon  is  always  quadrivalent,  hydrogen  uni- 
valent;  and  oxygen  has  been  taken  as  bivalent. 


184 


Albert  P.  Mathews 


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Value  of  "a"  of  -van  der  Waals'  Equation  185 

It  will  be  seen  in  Table  III  that  C  has  a  mean  value  of  2.98  X 
io~37  for  the  twenty- six  non-associating,  or  nearly  non-asso- 
ciating, substances  studied  by  Young.  The  greatest  devia- 
tion from, the  mean  is  octane  on  the  one  side,  which  deviates 
a  little  more  than  four  percent;  and  on  the  other,  fluorben- 
zene,  which  deviates  6  percent,  methyl  isobutyrate  deviating 
a  little  over  3  percent,  and  brom-  and  iodobenzene.  The 
deviation  of  the  last  two  substances,  about  7  percent,  may,  I 
think,  be  disregarded  since  the  critical  temperature  and  pres- 
sure were  estimated  and  not  directly  determined;  the  critical 
data  are  therefore  less  certain.  The  other  twenty-one  sub- 
stances do  not  deviate  more  than  3  percent  from  the  mean. 
The  cause  of  the  deviation  of  fluorbenzene  is  uncertain,  but 
there  is  a  regularity  in  the  other  deviations  which  suggests 
that  the  size,  shape,  or  compressibility  of  the  molecule  may 
play  a  slight  role  in  determining  the  critical  data,  or  the  co- 
efficients of  our  formulas.  For  it  appears  that  M2K,  and 
hence  C,  is  always  lower  in  the  iso-compounds  than  in  the  cor- 
responding normal  compounds.  Diisobutyl  has  C  of  the  mean 
value,  whereas  normal  octane  has  a  high  value  for  C;  a  similar 
relationship  exists  between  diisopropyl  and  hexane;  and  be- 
tween iso-  and  normal  pentane.  Some  of  this  difference 
would  disappear  if,  instead  of  taking  v0  equal  to  vc/4,  I  had 
used  the  accurate  ratio  computed  from  the  law  of  rectilinear 
diameter.  Thus  V0  of  isopentane  is  only  Vc/3-92;  while 
that  of  pentane  is  Vc/3-96  and  octane  is  Vc/4.°4-  The  sub- 
stitution of  these  values  for  V0  in  computing  M2K  would  have 
made  C  of  isopentane  2.98;  of  pentane,  3  . 03 .  The  difference 
is  not  entirely  due  then  to  this  factor.  It  seems  more  proba- 
ble to  me  that  bc  is  not  always  exactly  the  same  fraction  of 
Vc  and  that  consequently  the  coefficients  of  the  formulas  used 
in  computing  M2K  are  not  exactly  the  same  in  all  substances. 

Notwithstanding  x  these  slight  deviations,  the  constancy 
of  C  is  certainly  remarkably  good  and  shows  beyond  ques- 
tion, I  think,  that  a  close  connection  exists  between  molecu- 
lar cohesion  and.  the  molecular  weight  and  number  of  valences 
in  the  molecule. 


1 86 


Albert  P.  Mathews 


w 


used 
M2K 


U 


"o 

X 


0   y 

6 


O  O    CO 

... 

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. 


co^,    CN    ',  Q  »-4   ;  .    M.  « 

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c^>">r^!ll  co  co 

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CL,n          .-Pn    •-.-•- 

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CN          COCOCOCNCOCNCNCMCOCOCNCOCO         COCN 


10 

co 

<NGv 


w 
S 


1-1  ON  O    M    CN 


t^OO    u->  in  t^  uo          ON  GO  -*   00    t^   ON  CO 

co  rh^o  voooo        O<N         «-•   10  co  10  O    *5 

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CN^O<NOO(N»-iOO    ONOO    ONQNOfN          I^I-H          ^OOChcoON^ 

(N    <->  \O    O    ON 


. 

CO         cococococococococococococo         coco         cOcOcocOcO^ 


u     u"uuucjcjuuuucruu     uo     DOcToo0  3 


! 


1>  .= 

U 


— 

a>'n.;=i'o 

liiil 


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C   a; 

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t^QO    ON  O    -i 
HH     .-(     1-1     CS     CN 


Value  of  "a"  of  van  der  Waals'  Equation  187 


vO 


CO 


ii 


«« 


o°° 


0^ 
^ 


10  rj-  o   '-'   O 


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ON-IOOOOO         ON(N«-I>-IOOQNO 


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to 

CO  ^h          ON 


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co 


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CO  to  O  00    r^OO  OO    rf  M 

to  *-O  ^^  ^O  *-O  ^O  *-O  ^O  *O  *-O  *O  *-O  ^O     ^O  ^^  "^~  ^f"  to  to  to 

coco  CO  CO  .CO  CO  CO  CO  cOcOcOcOcO    cOcOcOcOcOcOcO 


vOO1^- 
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00 

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1 88  Albert  P.  Mathews 

Table  IV  is  a  summary  of  the  values  of  C  computed  for 
forty-one  other  substances,  of  many  of  which  the  critical 
data  are  not  so  accurately  known  as  those  included  in  Table 
III.  Since  for  most  of  these  substances  dc  and  Vc  were  not 
given  in  the  lyandolt-Bornstein-Meyerhoffer  tables,  I  com- 
puted Vc  by  the  formula  VCPC/TC  ==  21.92  and  then  M2K 
by  the  formula  M2K  ••  3.594  X  icT40  VCTC.  The  values  of 
Vc  so  computed  are  of  course  not  so  accurate.  Wherever 
the  critical  volume  or  density  was  given  it  was  used.  In  a 
few  cases,  which  are  specified,  M2K  was  obtained  by  dividing 
the  value  of  "a,"  given  by  Guye  and  Mallet,  by  N2,  i.  e., 
(2.77  X  io19)2. 

While  the  values  are  thus  less  certain  and  the  deviations 
somewhat  greater,  the  mean  value  of  all  is  what  it  was  for  the 
other  substances,  i.  c.,  C  ••  ••  2.98  X  io"37.  The  values  are 
surprisingly  uniform.  It  will  be  noticed  that  the  more  com- 
plex substances  such  as  diphenyl  and  diphenyl  methane  have 
C  a  little  high.  This  may  possibly  be  due  to  slight  associa- 
tion or  quasi-association  in  these  substances  With  this 
and  one  or  two  other  exceptions  the  uniformity  of  C  is  marked. 

All  substances  known  to  be  associating  give  a  value 
for  C  higher  than  2.98  X  io~37  when  M2K  is  computed  by 
the  same  formulas  as  for  normal  substances,  and  the  weight 
and  valence  used  in  computing  C  are  those  of  the  normal 
non-associated  molecule.  This  result  is  to  be  anticipated, 
since  in  these  substances  the  molecular  weight  and  valence 
do  not  remain  the  same  throughout  the  temperature  interval. 
The  computation  of  M2K  from  the  critical  data  is  uncertain 
in  the  case  of  associating  substances  for  the  reason  that  there 
is  no  certainty  that  the  coefficients  of  the  formulas  are  the 
same  for  these  substances  as  for  normal  substances.  Although 
the  figures  for  M2K  are  thus  uncertain,  I  have  nevertheless 
calculated  M2K  by  the  usual  formula  in  order  to  show  that 
these  substances  deviate  in  the  direction  we  should  expect 
from  the  value  of  C  found  in  normal  substances.  The  re- 
sults are  given  in  Table  V : 


Value  of  "a"  of  van  der  Waals'  Equation  189 


Cn  4^.  Co    to    HH    O^O    CO^J    ONCn  4^  Co    to    H< 


- 


i 


^         D- 

d»        ft) 
i-t 

O 


2.  2- 


PPP  2  Q  W  2  p  op  ppp  QP 

tn  K  ffi  w  «  t/)  B  B  B  B.B  Bal"  B 


-0 


as    o  °°b 


i  i  i 

CoCoCoCoCoCoCoCoCoCoCoCoCoCoCo 
CnCnCnCnCnCnCnCnCnCnCnCnCnCnCn 

•<!  OOVO  *-tCo  O  O  OO^O^O"^JCn  Cn  Co  ON 

ON  O\4^  ^  O  004^  Cn  -^  ON  ^J  ON  ON  Co  to 

t— *  *^j  ^  ^j  to  ON  **J  4^  *^J  ^O  Cn  Co  ^J  ON  ON 

O    O  Cn  MvOCnCoCnCnCo    OOtO^O    O*^J 


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•^j  Cn    to    •     Cn  O  O 

•       •      -•    00--  -•  -• 

co  ^r        -  •   ..  .,  ., 


||   4^  -^J  VO    >-- 

Cn  ON  K)    O    •-" 

Cn  4^.                 Cn 
to 

CO 
Cn 


xxxxxxx 


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o     o     o     o 


190  Albert  P.  Mathews 

I  have  also  calculated  the  value  of  M2K  and  the  quotient 
C  of  a  number  of  other  substances  from  the  surface  tension 
measurements  of  Ramsay  and  Shields.  From  the  surface 
tension,  the  critical  temperature  may  be  calculated  approxi- 
mately by  the  rule  of  Botvos,  revised  by  Ramsay  and  Shields, 
namely,  K(TC  —  T  —  6)  =-  S(M^)2/3,  where  S  is  the  surface 
tension  in  dynes  at  the  absolute  temperature  T  and  Mi;  the 
molecular  volume.  Having  thus  found  T0  the  fraction  T/TC 
may  be  calculated  for  any  temperature  and  by  interpolation 
from  the  curve  expressing  the  relation  between  T/TC  and  V/VC, 
V/VC  may  be  found  and  from  this  Vc  may  be  calculated  if 
V  is  known.  We  thus  obtain  the  theoretical  critical  volume. 
From  Vc  and  Tc  the  value  of  M2K  may  be  calculated  either 
by  the  surface  tension  formula  or  the  formula  M2K  *  •  VCTC 
3.594  X  io~40.  I  shall,  in  the  first  place,  show  how  exactly 
the  law  correlating  M2K  with  weight  and  valence  holds  for 
some  substances  which  do  not  contain  chlorine  but  contain 
elements  of  which  the  valence  is  fairly  certain.  Some  of 
these  substances  associate  slightly.  The  results  are  summar- 
ized in  Table  VlX 

From  Table  VI  it  may  be  seen  that  the  values  obtained  for 
C,  although  less  reliable  than  those  from  the  other  tables, 
nevertheless  agree  well  with  the  mean  of  about  3  X  io~37. 

The  substances  marked  associating  in  the  above  table 
were  found  to  be  so  by  Dutoit  and  Mojoiu,1  who  determined 
the  association  and  calculated  the  mean  molecular  weight  at 
various  temperatures. 

There  are  two  sources  of  uncertainty  in  computing  "a" 
and  M2K  for  the  simplest  gases;  the  first  is  the  uncertainty 
of  the  critical  data  of  some  of  them;  and  the  second,  the  un- 
certainty that  the  coefficients  of  the  formulas  hitherto  used 
for  calculating  these  values  remain  the  same  for  the  gases. 
If  the  usual  formula  for  "a"  be  used,  by  which  "a"  is  calcu- 
lated from  the  pressure  and  temperature,  the  formula  being 
derived  from  certain  assumptions  as  to  the  value  of  the  crit- 

1  Dutoit  and  Mojoiu:  Constante  de  capillarite  et  poids  moleculaire.  Jour. 
Chim.  Phys.,  7,  169  (1909). 


Value  of  "a"  of  van  der  Waals'  Equation 


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192  Albert  P.  Mathews 

ical  coefficient,  the  value  of  C  is,  for  fairly  complex  substances, 
about  2.80  X  io"37;  but  in  the  simple  gases,  such  as  N2O, 
H2,  O2,  N2,  etc.,  it  is  uniformly  lower  and  about  2.25.  The 
question  is,  therefore,  whether  this  formula  does  not  give  an 
exact  value  for  M2K,  or  whether  the  relation  of  M2K  to  the 
weight  and  valence  is  only  approximate  and  does  not  remain 
the  same  for  the  simple  substances.  It  is  possible  that  the 
ratio  27/64  in  the  "a"  formula  is  not  the  same  for  all  sub- 
stances, but  may  vary  a  little  with  the  complexity,  or  com- 
pressibility, of  the  molecule.  To  solve  this  uncertainty,  T 
have  computed  M2K  directly  from  the  surface  tension  of  the 
liquid  gases  by  the  half  empirical  formula  which  holds  pretty 
well  for  more  complex  substances:  M2K(i/7;1 — i/^)  = 
3SV*[(TC  —  6)/(Tc  --  T—  6)]2/»  I  have  used  the  data  of 
Baly  and  Donnan  in  this  calculation.  I  also  calculated  M2K 
from  the  latent  heat  of  vaporization  from  figures  given  by 
Dewar  in  his  article  on  Liquid  Gases  in  the  Encyclopedia 
Britannica,  by  the  formula:  L  —  E  =  a(i/V1  —  i/VJ.  a  = 
N2M2K.  This  formula  neglects  the  heat  used  in  the  expan- 
sion of  the  molecules  in  passing  from  the  liquid  to  the  vapor. 
It  generally  gives,  therefore,  a  value  of  M2K  somewhat  too 
high.  I  have  also  computed  M2K  by  the  usual  formulas  in- 
volving Vc  and  Tc  instead  of  Pc  such  as  the  surface  tension 
formula.  In  Table  VII  I  have  included  the  values  thus  cal- 
culated for  hydrogen,  using  successively  the  critical  data  of 
Olszewski  and  Dewar. 

It  is  evident  that  a  considerable  uncertainty  in  the  case 
of  hydrogen  arises  from  the  uncertainty  of  the  critical  data. 
I  think  the  PCV2C  formula  gives  too  high  results.  If  we  take 
the  mean  of  all  it  would  be  —37 .88161.  With  the  valence  2 
and  the  weight  2  this  would  give  for  "c"  a  value  of  3.02  X 
io~37,  which  is  close  to  the  value  obtained  before. 

I  have  made  similar  calculations  in  the  case  of  oxygen, 
nitrogen,  carbon  dioxide  and  nitrous  oxide.  For  the  sake  of 
brevity  I  omit  these  and  give  in  Table  VIII  only  the  mean 
value  for  M2K  for  each  gas. 

It  is  clear  from  Table  VIII  that  with  the  exception  of  car- 


Value  of  "a"  of  van  der  Waals'  Equation  193 


CO  CO  CO  CO  CO  CO  CO 

^J  -<t  ^1  ^1  ^4  ^J  ^1 

ODVO  00  00  OOVO  00 
Cn  \O  ^4  -^  O  Cn  to 

tO   t-H  ^J   HH   O   ON  Ki 

-fi.  HH  Cn  vo  M  K)  ^| 

N)  00  00  O  4*  M  ON 


V 

X 


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o  *  I  o 

I   °  o  I   \ 


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Co  Co  Co  Co  Co  Co 
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O  O  O  Cn  Cn  Cn 


Cn  Cn  Cn 


Cn  Cn  Cn  4^  -fi.  4^. 
to  K)  to  to  K>  to 


i 
8 


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194 


Albert  P.  Mathews 


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Value  of  "a"  of  van  der  Waals'  Equation  195 

bon  monoxide,  which  is  hopelessly  aberrant  if  carbon  and  oxy- 
gen have  a  higher  valence  than  one,  the  value  of  C  comes  close 
to  the  value  found  in  other  substances,  namely,  2.98  X  io~37. 
It  is  true  that  in  making  the  calculation  I  have,  in  one  or  two 
instances,  used  other  valence  numbers  than  those  generally 
attributed  to  the  elements.  Thus  chlorine  is  trivalent.  But 
I  shall  show  in  a  subsequent  paper  that  chlorine  is  always 
trivalent  in  its  organic  compounds;  nitrogen  in  the  gaseous 
form  is  univalent,  while  it  is  bivalent  in  nitrous  oxide;1  but 
both  these  valences  have  already  been  ascribed  to  nitrogen. 
Oxygen  cannot  have  more  than  two  valences  in  the  molecule. 
The  value  I  have  taken  for  M2K  is  certainly  as  high  as  the 
facts  warrant  and  the  critical  data  seem  reliable.  I  believe 
that  the  conclusion  is  justified  that  oxygen  is  monovalent 
in  its  gaseous  form.  The  surprising  fact  is  the  value  for  car- 
bon dioxide.  The  carbon  cannot  be  more  than  bivalent 
here,  giving  a  kind  of  peroxide  formula,  if  carbon  dioxide  is 
to  follow  the  rule.  On  the  whole,  the  gases  agree  well  with 
the  results  already  obtained  for  C. 

In  a  subsequent  paper  I  shall  show  that  all  chlorine  com- 
pounds also  follow  the  rule  if  the  chlorine  be  taken  trivalent; 
and  that  there  is  good  reason,  from  quite  independent  sources, 
to  attribute  a  valence  of  three  to  chlorine.  The  valences  of 
sulphur,  nitrogen  and  the  argon  group  will  also  be  considered 
separately. 

In  closing  it  may  be  pointed  out  that  the  law  just  estab- 
lished can  be  used  to  determine  the  number  of  valences  in  a 
molecule  if  M2K  of  the  substance  is  known,  or  if  its  critical 
data  are  known,  as  follows:  If  the  computation  is  made 
from  the  approximate  values  of  "a"  given  in  the  Landolt- 
Bornstein-Meyerhoffer  tables,  which  were  computed  by  the 
formula:  a  27^7(64  X  273'  X  Pc),  proceed  by  the 
following  formula:  (i)  Valence  number  ••  ••  (a)3/2  X  3.2  X 
io5/(Mol.  Wt.).  Or,  if  the  calculation  is  made  from  the 
critical  data,  the  following  formula  will  serve: 

1  Possibly  nitrogen  is  univalent  in  this  gas,  but  the  oxygen  is  quadriva- 
lent, having  two  free  valences. 


196 


Albert  P.  Mathews 


(2)  Val.  number  =  =  0.0043  Tsc/Pcs/*(Mol.  Wt.);  or,  if 
the  calculation  is  made  from  the  temperature  and  volume: 
(3)  Val.  number  =  4.21 -X  iQ-5  X  (VcTc)8/*/(Mol.  Wt.). 


-37.56 


Fig.  i  —Showing  the  relationship  between  the  logarithm  of  M2K  and  the 

logarithm  of  the  product  of  the  molecular  weight  by  the 

number  of  valences 

In  these  formulas  Vc  is  the  critical  volume  of  a  gram  mol.  in 
cubic  centimeters;  Tc,  the  absolute  critical  temperature; 
and  Pc  the  critical  pressure  in  atmospheres. 


Value  of  "a"  of  van  der  Waals'  Equation  197 

How  accurately  the  number  of  valences  can  be  calculated 
by  the  first  formula  is  shown  by  Table  IX,  which  is,  of  course, 
little  more  than  a  rearrangement  of  the  results  already  stated 
in  the  preceding  tables,  except  that  in  this  instance  I  have 
used  the  approximate  values  of  "a"  given  in  the  Landolt 
tables  computed  by  the  formula  a  =  27Tc2/(64  X  273*  X  Pc). 

An  inspection  of  Table  IX  will,  I  think,  convince  all  that 
molecular  cohesion,  as  expressed  by  the  value  "a"  of  van 
der  Waals'  equation,  is  a  function  of  the  weight  and  valence 
of  the  molecule.  If  "a"  is  calculated  for  all  these  substances 
from  the  critical  temperature  and  pressure  by  the  formula : 
a  =  =  27T2C/64PC  x  2732,  the  number  of  valences  is  calculated, 
with  a  remarkable  degree  of  approximation,  from  the  as- 
sumption that  a  --=  CN2Wt2/3Val2/3,  by  the  formula  given  at 
the  beginning  of  the  table.  It  will  be  noticed  that  all  asso- 
ciating substances  give  by  this  formula  a  larger  number  of 
valences  than  that  calculated  for  the  normal  substance,  and 
that  the  degree  of  excess  of  trie  number  of  valences  is  more 
or  less  proportional  to  the  degree  of  association.  Thus 
the  largest  excess  is  in  the  case  of  water,  where  the  cohesion 
calls  for  22  valences,  and  in  some  of  the  nitriles;  whereas  sub- 
stances like  the  esters,  which  associate  very  little,  have  only 
a  few  valences  in  excess.  Putting  aside  associating  substances, 
of  which  the  deviation  from  the  rule  is  to  be  expected,  there 
are  certain  exceptions  characteristic  of  certain  observers. 
The  coefficient  3.2  X  io5  was  taken  from  Young's  data  for 
ether.  It  will  be  seen  that  always  Nadejdine's  critical  con- 
stants give  a  value  for  "a"  lower  than  Young's,  where  both 
observers  have  worked  on  the  same  substances.  So  the  sub- 
stances computed  from  Nadejdine's  critical  data  generally 
show  a  deficit  of  two  or  three  valences  to  the  molecule.  I 
think  in  these  cases  Young's  values  are  to  be  accepted.  Vin- 
cent and  Chappuis'  determinations,  also,  generally  come  a 
little  low,  though  they  are  very  close,  The  main  constant 
deviation  from  the  law  is  to  be  observed  in  the  case  of  sub- 
stances like  methane  and  hydrogen  of  very  low  molecular 
weight  and  great  molecular  simplicity;  and  those  substances 


198 


Albert  P.  Mathews 


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202  Albert  P.  Mathews 

studied  by  Guye  and  Mallet1  of  very  high  molecular  weight 
and  complexity,  such  as  durol,  cymol,  diphenyl  and  diphenyl 
methane.  So  far  as  I  can  find,  the  evidence  is  that  these  sub- 
stances associate  but  little;  so  the  deviationc  annot  be  attrib- 
uted to  that.  It  may  be  that  Guye  and  Mallet's  determina- 
tions have  some  constant  source  of  error  which  brings  them 
higher  than  determinations  on  similar  substances  by  Altschul, 
but  I  do  not  think  this  is  the  explanation  of  the  facts.  The 
fact  that  the  deviation  is  in  the  opposite  direction  in  the  sim- 
plest from  what  it  is  in  the  most  complex  substances  leads 
me  to  believe,  as  stated  on  page  192,  that  the  calculation  of 
"a"  by  this  formula  may  be  at  fault. 

While  there  can  be  little  doubt  that  this  formula  gives  a 
value  for  "  a  "  approximately  correct  for  all  normal  substances, 
as  van  der  Waals  has  recently  reaffirmed,  and  accordingly 
that  the  ratio  27/64  is  at  least  approximately  true  for  all 
substances,  yet  it  is  not  certain  that  this  ratio  is  exactly  con- 
stant for  all  substances.  It  can  only  be  strictly  justified  for 
the  simplest  substances  in  which  "6,"  the  volume  of  the  mole- 
cule, is  constant.  I  believe  it  to  be  far  more  likely  that  this 
ratio  changes  a  little  with  progressive  increase  in  molecular 
complexity,  and  a  resulting  greater  compressibility  of  the 
molecule,  as  indeed  van  der  Waals  has  suggested,  than  that 
the  law,  which  I  have  here  attempted  to  establish,  of  the  de- 
pendence of  cohesion  on  molecular  weight  and  valence  holds 
strictly  only  for  substances  of  medium  complexity.-  This  re- 
lationship of  cohesion  to  these  two  molecular  properties  seems 
so  probable  and  so  fundamental  that  I  believe  we  may,  with 
some  confidence,  anticipate  that  if  it  holds  at  all,  it  holds 
everywhere. 

It  seems  not  worth  while  to  consider  this  question  further 
until  it  is  decided  whether  "a"  is  in  all  instances  determined 
by  the  formula  just  mentioned;  or  whether  the  ratio  27/64 
is  true  only  for  the  simplest  substances  with  constant  molec- 
ular volume,  that  is  a  constant  "  6; "  and  that  for  more  complex 


1  Guye  and  Mallet:  Comptes  rendus,  133,  1288  (1901);  134,  168  (1902). 


Value  of  "a"  of  van  der  Waals'  Equation  203 

and  compressible  molecules  it  must  be  slightly  diminished 
as  the  complexity  and  compressibility  increases.  If  the  lat- 
ter shall  prove  to  be  the  case,  then  most  of  the  exceptions 
noted  in  the  preceding  pages  would  disappear.  The  substitu- 
tion of  the  value  for  "M2K"  computed  by  my  formula  from 
the  surface  tension  would  have  given  a  much  closer  agreement 
of  the  calculated  and  observed  valence  numbers,  but  I  wished 
to  show  that  the  law  holds  at  least  approximately  even  though 
we  use  the  approximate  values  of  "a"  computed  by  the  usual 
formula. 

The  constant  2.98  X  io~37  discovered  in  the  foregoing 
pages,  is  evidently  the  factor  M2K  of  a  substance  of  unit 
molecular  weight  and  unit  valence.  No  such  substance  as 
this  is  known,  but  hydrogen  with  a  weight  and  valence  of 
two,  and  helium  with  a  weight  of  four  and  valence  of  unity  (?) 
have  values  of  M^K  not  very  different.  Thus  for  hydrogen,1 
M2K  is  between  3.16  and  7.72  X  io~37;  and  M2K  of  helium 
lies  between  the  same  two  values  probably.  The  value  of 
2  .98  X  icT37  is  of  the  order  of  magnitude  of  the  gravitational 
attraction  of  two  average  molecules.  Thus  at  20°  two  mole- 
cules of  ether  in  the  liquid  state  attract  each  other  gravita- 
tionally  with  a  force  of  3.11  X  io~37  dynes.  The  similarity 
of  these  values  is,  however,  probably  only  a  coincidence. 

Conclusion 

The  facts  presented  in  the  foregoing  pages  enable  us  to 
draw  the  general  conclusion:  The  "mass"  of  cohesion  of  a 
molecule  is  everywhere  proportional  to  the  cube  root  of  the 
molecular  weight  multiplied  by  the  cube  root  of  the  number 
of  valences  in  the  molecule.  Or,  to  put  it  in  another  way, 
"a"  of  van  der  Waals'  equation  for  one  cc.  of  gas  under 
standard  conditions  is  equal  to  2.98  X  io~37  X  Mol.  Wt2/3  X 
Valences27'  X  (2.77  X  io19)2  dynes;  or  this  number  divided 


1  M2K  for  H2  computed  from  the  value  "a"  given  by  Landolt-Bornstein 

27  T  2 

is  5-55  X   icr37.     This  was  computed  by  the  formula  a  = 

64  X  273     X  rc 


2O4  Albert  P.  Mathews 

by  1.0135  X  io6  atmospheres.  This  formula  gives  a  value 
for  "a"  somewhat  higher  than  the  ordinary  formula  and  it 
may  be  that  the  coefficient  should  be  taken  a  little  lower. 

The  theoretical  significance  of  this  relationship  of  cohe- 
sion to  the  molecular  weight  and  the  number  of  valences 
is  very  interesting,  but  I  shall  reserve  its  consideration  for  a 
subsequent  paper. 

University  of  Chicago 


THE  VALENCE  OF  CHLORINE  AS  DETERMINED  FROM 

THE  MOLECULAR  COHESION  OF  CHLORINE 

COMPOUNDS 


BY  ALBERT  P.  MATHEWS 

Since  molecular  cohesion  is  a  function  of  the  molecular 
weight  and  the  number  of  valences  in  the  molecule,1  we  may 
use  the  cohesion  for  the  purpose  of  determining  the  valence 
of  elements;  and  in  this  paper  I  shall  consider  chlorine,  although 
something  will  be  said,  also,  about  the  other  halogens. 

It  is  generally  believed,  at  the  present  time,  that  the 
valence  of  chlorine  is  not  fixed,  but  varies  in  different  com- 
pounds from  one  to  seven.  In  its  organic,  and  some  inor- 
ganic compounds,  and  in  its  elemental  form  it  is  generally 
represented  as  univalent;  whereas  in  the  chlorates  it  is  sup- 
posed to  be  pentavalent;  and  in  the  perchlorates  it  is  hepta- 
valent. 

That  chlorine  even  in  such  compounds  as  chloroform, 
where  it  replaces  univalent  hydrogen,  may  not  be  univalent 
is  indicated  by  the  action  of  chlorine  compounds  on  light. 
Drude,2  reasoning  that  it  must  be  the  valence  electrons  of 
compounds  which  would  have  a  period  of  vibration  sufficiently 
long  to  respond  to  light  waves,  worked  out  a  modification 
of  the  Ketteler-Helmholtz  dispersion  formula  which  enabled 
an  approximate  computation  of  the  number  of  electrons  in- 
fluencing dispersion  in  the  molecule.  He  found  that  in 
many  cases  this  number  was  close  to  the  total  number  of 
valences  in  the  molecule;  but  in  the  case  of  compounds  con- 
taining chlorine  and  fluorine,  the  number  of  such  light-re- 
fracting valences  was  always  greater  than  in  the  correspond- 
ing hydrogen  compounds,  and  he  inferred  from  this  that 


1  Mathews:     "The  Relation  of  the  Constant  "a"  of  van  der  Waals'  Equa- 
tion to  the  Molecular  Weight  and  the  Number  of  Valences  in  the  Molecule," 
Jour.  Phys.  Chem.,  17,  181  (1913). 

2  Drude:  "Optische  Eigenschaften  und  Elektronen  Theorie,"  Annalen  der 
Physik,  [4],  14,  677  (1904). 


The  Valence  of  Chlorine  253 

these  elements  must  be  polyvalent,  and  not  monovalent,  as 
they  were  usually  supposed  to  be.  This  conclusion  of  Drude's 
was  confirmed  by  Pascal1  both  by  the  dispersion  method  of 
computing  valence  and  by  a  study  of  the  diamagnetic  proper- 
ties of  halogen  compounds,  the  diamagnetic  properties  having 
been  shown  to  be  related  to  the  number  of  valences  in  the 
molecule.  Pascal  concluded  that  fluorine,  in  organic  com- 
pounds at  any  rate,  was  univalent;  but  chlorine  and  the  other 
halogens  were  polyvalent,  and  probably  chlorine  was  tri- 
valent.  Traube,2  in  a  study  of  the  relationship  between  the 
molecular  refraction  of  compounds  and  the  number  of  their 
valences,  found  that  for  most  compounds  the  molecular  re- 
fraction of  Bruhl  divided  by  the  number  of  valences  in  the 
molecule  was  a  constant,  or  nearly  such,  in  all  saturated  com- 
pounds; but  in  the  case  of  molecules  containing  the.  halogens 
it  was  necessary  to  ascribe  several  valences  to  the  halogens 
to  obtain  this  constant.  He  attributed  seven  valences  to 
chlorine,  and  had  to  make  still  other  assumptions  for  bromine 
and  iodine  to  bring  them  into  line. 

Several  chemists,  also,  have  in  the  past  ascribed  several 
valences   to  chlorine.     Thus  Meldola3  wrote   the  formula  of 

CH3\ 

methylether    hydrochloride,    in    the   form  >O  =  Cl  —  H, 

CH 


3 


with  chlorine  trivalent;  Nef4  represented  elemental  chlorine 
as  trivalent,  but  combined  chlorine  generally  as  monovalent; 
and  recently  Thiele5  has  especially  emphasized  the  reserve, 
or  extra,  valences  of  iodine  and  bromine,  although,  as  a  rule, 
he  represents  chlorine  as  univalent.  Even  in  sodium  chlor- 
ide it  is  not  certain  that  the  chlorine  is  univalent,  since  it  is 


1  Pascal:  "Recherches  magneto-chimiques  sur  la  structure  atomique  des 
halogenes,"  Comptes  rendus,  152,862  (1911);  "Sur  un  mode  de  controle  optique 
des  analyses  magneto-chimiques,"  Ibid.,  152,  1852  (1911). 

2  Traube:  "Valency,    Lichtbrechung  u.  volume,"  Ber.  chem.  Ges.  Berlin, 
40,  130  (1907). 

3  Meldola :  I  have  mislaid  this  reference  and  have  not  been  able  to  find  it 
again. 

4  Nef:  Liebig's  Ann.,  298,  205  (1897). 

6  Thiele  and  Peter:  Ber.  chem.  Ges,  Berlin,  38,  2842  (1905). 


254  Albert  P.  Mathews 

known  that  sodium  chloride  will  add  iodine,  presumably  by 
the  extra  valences  of  the  chlorine.1 

There  is  good  ground,  therefore,  for  doubting  whether 
chlorine  is  ever  monovalent.  This  question  can  be  tested 
easily  by  the  cohesion  method. 

Before  proceeding  to  the  actual  computations  it  must 
be  decided  whether  the  cohesion  method  detects  only  valences 
actually  employed  in  binding  atoms  together,  or  stretching 
between  the  atoms;  or  whether  it  detects  in  addition  the  re- 
serve valences;  and  also  valences  which  do  not  extend  to 
atoms,  but  which  are  open,  in  an  active  form,  and  ready  to 
combine  if  the  opportunity  arises.  It  is  clear  from  my  former 
paper  that  concealed,  polarized,  resting  or  reserved  valences 
do  not  play  any  part  in  cohesion ;  or,  at  any  rate,  they  are  not 
to  be  counted  in  the  number  of  valences  affecting  the  cohesion. 
Thus  oxygen  has  certainly  two  reserve  valences  which  are 
usually  in  an  inactive  or  resting  state.  In  many  compounds 
examined,  not  more  than  two  valences  could  be  attributed 
to  the  oxygen  as  affecting  its  cohesion.  These  two  reserve 
valences  played  no  role  as  long  as  they  were  inactive.  Sim- 
ilarly, nitrogen  has  the  power  of  opening  up  at  least  seven 
valences,  but  it  was  actually  found  that  only  one,  two  or 
three  valences  played  a  role  in  the  cohesion  of  the  nitrogen 
compounds,  depending  on  how  many  active  valences  the  atom 
had.  The  reserve,  or  inactive,  valences  played  no  part. 
Carbon  is  usually  quadrivalent,  but  it  is  suspected  of  having 
the  power  of  becoming  hexavalent;  but  the  number  of  valences 
active  in  carbon  compounds  was  always  two,  or  four.  If 
these  reserve  valences  of  carbon  exist  they  do  not  affect 
cohesion.  Sulphur,  too,  although  it  may  be  hexavalent,  has 
only  four  of  its  valences  playing  a  part  in  the  cohesion  of  sulphur 
dioxide;  the  two  reserve  valences  are  inactive  on  the  cohesion. 

It  is  clear,  then,  that  the  cohesion  does  not  detect,  and 
consequently  it  is  not  affected  by,  those  reserve  valences 
which  are  polarized,  or  resting,  or,  which  are,  as  it  were, 
like  antennae,  withdrawn  or  folded,  within  the  atom. 

1  See  Friend:  "The  Theory  of  Valency,"  London,  1909,  pp.  58  et  seq. 


The  Valence  of  Chlorine  255 

But  valences  may  conceivably  exist  in  an  active  state 
not  stretching  between  atoms,  but  extending  outward  from 
the  atom  and  in  a  condition  to  unite  with  other  atoms.  These 
are  active  valences.  For  example,  we  may  expect  the  va- 
lences on  the  atoms  of  a  dissociated,  monovalent  gas  to  be 
in  this  condition.  Such  atoms  would  naturally  be  very  ac- 
tive chemically  and  we  should  expect  the  cohesion  of  such 
particles  to  be  affected  by  this  condition.  There  are  many 
evidences  that  this  is  actually  the  case  and  that  valences  of 
this  kind  are  detected  by  cohesion  and  will  be  included  in 
the  number  of  valences  computed  from  the  cohesion  as  ex- 
isting in  the  molecule.  This  is  well  shown  in  the  argon  group, 
which  I  shall  discuss  later,  in  which  it  appears  that  there  are 
two  such  active  valences  in  argon,  krypton,  and  probably 
xenon.  It  appears  to  be  the  case,  too,  in  unoxidized  sulphur 
compounds  such  as  ethyl  sulphide,  as  I  shall  show  in  a  subse- 
quent paper.  And  there  is  evidence  elsewhere  that  these 
open-  or  active  valences  affect  cohesion,  although  they  do  not 
stretch  between  the  atoms  of  the  same  molecule.  It  is,  then, 
active  vajences,  and  valences  actually  employed  in  binding 
together  the  atoms  of  the  molecule,  which  affect  molecular 
cohesion.  It  is  only  the  number  of  such  valences  which  the 
cohesion  enables  us  to  compute,  and  it  is,  of  course,  exactly 
for  this  reason  that  the  method  has  so  great  a  value. 

We  may  then  be  certain  that  if  we  find  the  valence  of 
chlorine  to  be  three  and  the  compounds  are  not  associating, 
those  three  valences  are  not  free,  but  are  actually  extending 
between  atoms  in  the  molecule,  and  if  we  wish  an  accurate 
graphic  formula  of  the  compound  we  must  represent  these  ties. 

The  method  of  measuring  the  number  of  valences  is  to 
compute  the  number  from  "a"  of  van  der  Waals'  equation, 
or  from  what  I  have  called  the  square  of  the  cohesive  mass, 
or  M2K,  a  factor  which  is  equal  to  "a",  divided  by  the  square 
of  the  number  of  molecules  in  the  volume  of  fluid  for  which 
"a"  has  been  taken.  The  method  of  computing  M2K  is 
given  in  the  previous  paper.  The  formula  employed  is 
M2K  .-  2.98  X  io~37  (Mol.  Wt.  X  Valences)273.  Or:  Number 
of  Valences  -  (M2K)3/2  X  6.147  X  io54/(Mol.  Wt.). 


256 


Albert  P.  Mathews 


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The  Valence  of  Chlorine 


257 


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258 


Albert  P.  Matheivs 


To  show  how  closely  these  compounds  yield  the  con- 
stant "c,"  where  c  ---  M2K/(Mol.  Wt.  X  Valences)273,  Table 
II  is  appended.  "C"  was  found  in  a  previous  paper  to  be 
about  2.98  X  io~37  for  other  than  chlorine  compounds. 
Chlorine  is  throughout  considered  as  trivalent. 

TABLE  II. — "C"  CALCULATED  FOR  CHLORINE  COMPOUNDS.  CL  CON- 
SIDERED TRIVALENT  EXCEPT  IN  HYDROCHLORIC  ACID  AND 
PROPYL  CHLORIDE 


Substance 

Formula 

Va- 
lance 

CXio37 

Remarks 

I 

Carbon  tetrachloride         CC14 

16 

3-03 

2 

Stannic  tetrachloride        SnCl4 

16 

2.91 

3 

Germanium  tetrachlor- 

ide 

GeCl4 

16 

2.78 

All  4  chlorines 

• 

trivalent 

4 

Silicon  tetrachloride          SiCl4 

16 

2.86 

5 

Chloroform                          CHC13 

H 

2  .QO 

6 

Methyl  chloride                  CH3C1 

10 

2.97 

7 

Chlorine                               C13 

6 

2.96 

8 

Ethyl  chloride 

C2H5C1 

16 

3.06 

9 

Ethylene  chloride 

C2H4C12 

18 

3-15 

10 

Ethylidene  chloride 

C2H4C12 

18 

3-02 

ii 

Chlorbenzene 

C6H5C1 

32 

2.98 

12 

Thiosulfuryl  chloride 

S2C12             i  8 

3-23 

Some    associa- 

tion 

13 

Acetyl  chloride 

CH3COC1      1  6 

3  .  08     Slight  associa- 

tion 

14 

Chlorethyl  formate             C3H5C1O2      24 

2.96 

15 

Chloral   "                              CC13CHO 

20 

2.67 

16 

Thionyl  chloride 

SOC13 

H 

3-09 

Slight  associa- 

tion (sulphur 

hexavalent) 

17 

Sulfuryl  chloride 

SO2C12 

H 

2.97 

Sulphur  quad- 

rivalent 

18 

Propyl  chloride 

C3H8C1 

21 

2-93 

19 

Phosphorus  trichloride 

PC13 

1.6 

3-03 

20 

Phosphorus  oxychloride    POC13 

18 

2.99 

21 

Hydrochloric  acid              HC1            1     2  i  3.24  ;  Association  (?) 

Mean  (omitting  HC1,  S2C12  and  CC13CHO),  2.99 

The  answer  to  the  question  whether  chlorine  is  trivalent 
or  monovalent  is  given  in  no  indecisive  manner  by  the  method 


The  Valence  of  Chlorine  259 

of  determining  the  valence  from  the  cohesion,  as  is  shown  in 
columns  5  and  6  of  Table  I.  With  three  possible  exceptions, 
chlorine  is  seen  to  be  everywhere  trivalent.  The  possible  ex- 
ceptions are  hydrochloric  acid,  propyl  chloride  and  one  of 
the  chlorine  atoms  in  germanium  tetrachloride.  In  the  first, 
association  renders  the  valence  of  the  chlorine  somewhat 
doubtful;  in  other  words,  here  also  chlorine  may  be  trivalent. 
In  the  second,  propyl  chloride,  the  critical  data  may  be  wrong. 
They  were  determined  in  1886  by  Vincent  and  Chappuis, 
and  the  other  determinations  by  these  authors  give  generally 
a  value  for  "a"  slightly  lower  than  is  to  be  expected.  It  is 
not  impossible,  therefore,  that  a  redetermination  of  the  crit- 
ical data  for  this  substance  will  make  M2K  sufficiently  high 
to  make  the  chlorine  trivalent.  For  the  third  substance, 
germanium  tetrachloride,  I  can  find  but  one  determination 
of  the  critical  data  in  1887.  It  is  not  unlikely,  therefore,  that 
the  data  will  need  some  revision.  This  method  of  deter- 
mining the  valence  of  chlorine  confirms,  therefore,  the  con- 
clusions of  Pascal,  based  on  the  study  of  the  dispersion  and 
the  magnetic  properties,  that  chlorine  is  polyvalent,  and, 
further,  this  method  shows  it  to  be  beyond  doubt  generally 
trivalent. 

Moreover,  since  nearly  all  these  compounds  are  normal 
and  not  associating,  the  valences  of  the  chlorine  are  shown  to 
be  not  resting,  or  in  reserve,  and  not  dissociated  active  val- 
ences, but  actually  extending  between  the  atoms  of  the 
molecule.  I  have  indicated  in  column  8  of  Table  I,  some 
possible  structural  formulae  showing  how  these  valences  may 
be  extending  in  the  molecule.  Where  there  are  two  or  more 
chlorine  atoms  in  the  molecule,  no  serious  reconstruction  of 
the  graphic  formulae  is  required,  since  the  extra  valences  may 
be  pictured  as  reaching  between  the  chlorine  atoms;  but  where 
there  is  an  odd  number  of  chlorine  atoms  in  the  molecule, 
or  where  there  is  but  a  single  one,  then  a  fundamental  change 
must  occur  in  the  graphic  formula.  For  example,  in  ethyl 
and  methyl  chlorides,  the  formula  must  be  written  as  I  have 
indicated,  with  the  chlorine  joining  the  carbon  by  two  bonds 


260  Albert  P.  Mathews 

and  with  one  hydrogen  united  to  the  chlorine.  I  do  not  wish 
to  lay  stress  on  this  point  until  by  a  careful  determination 
of  the  critical  data  the  number  of  valences  in  the  molecule 
shall  have  been  exactly  determined,  but  it  may  be  pointed 
out  that,  if  methyl  chloride  be  written  as : 

H\ 

>C  =  C1— H, 

H/ 

the  reason  why  it  decomposes  into  methylene  and  hydrochloric 
acid  appears  at  a  glance,  since  such  a  double  bond  is  always 
a  source  of  weakness;  and  similarly  with  ethyl  chloride,  which 
would  be  in  reality  ethylidene  chlorhydrate,  decomposing  into 
ethylidene  and  hydrochloric  acid.  One  can  also  more  easily 
understand  in  this  way  the  decomposition  of  chloroform 
into  dichloro- methylene  and  hydrochloric  acid,  as  the  for- 
mula 

C1\ 

j  |    >C  =  C1— H 

CK 

shows.  Phosgen  will  arise  from  the  dichlormethylene  uniting 
with  oxygen. 

The  evidence,  then,  from  such  various  sources  as  the  be- 
havior, toward  light,  the  diamagnetic  properties  and  cohesion 
is  unanimous  that  chlorine  is  polyvalent  and  not  monovalent; 
many  of  the  chemical  and  physiological  properties  of  chlorine 
compounds  are  also  more  easily  understood  on  the  hypothesis 
of  its  trivalency.  We  may,  therefore,  conclude  that  in  all 
these  compounds  chlorine  is  trivalent. 

The  question  which  must  now  be  settled  is  no  longer 
whether  chlorine  is  trivalent,  but  whether  it  is  ever  mono- 
valent. It  is  certainly  trivalent  in  most  of  these  compounds 
in  which  it  was  supposed  to  be  monovalent;  it  is  trivalent  even 
in  its  elemental  state.  It  remains  to  be  seen  whether  it  is 
ever  monovalent.  In  hydrochloric  acid  it  would  appear  to 
be  monovalent;  but  it  is  exactly  here  that  association  takes 
place.  Is  it  without  significance  that  exactly  that  compound 
associates  which  has  but  one  of  the  valences  of  the  chlorine 


The   Valence  of  Chlorine  261 

satisfied  by  another  monovalent  atom?  Is  it  not  rather  more 
probable  that  this  is  the  cause  of  its  association,  the  other 
two  valences  being  not  closed,  but  out  and  active?  The  com- 
putation actually  shows  that  the  chlorine  is  here  also  tri- 
valent.  I  know  of  no  means  of  telling  whether  it  is  mono- 
valent or  trivalent  in  sodium  chloride.  But  it  is  not  impos- 
sible that  sodium  chloride  itself  is  a  highly  associated  sub- 
stance. Furthermore,  its  power  of  adding  iodine  indicates 
that  the  chlorine  may  be  trivalent.  Friend  also  states  that 
sodium  chloride  may  be  Na  —  Cl  =C1  --  Na. 

Concerning  the  valence  of  the  other  halogens,  the  facts 
are  too  scanty  and  the  data  too  unreliable  to  draw  a  conclu- 
sion from  the  cohesion,  except  perhaps  in  the  case  of  elemental 
bromine,  which  appears  to  be  univalent.  The  critical  data 
of  brombenzene  and  iodobenzene  were  not  directly  deter- 
mined by  Young,  but  computed  from  the  temperature,  pres- 
sure and  density  curves.  I  do  not  believe  that  they  are  en- 
tirely trustworthy,  since  the  number  of  valences  found  in  the 
molecule  is  too  small  even  if  these  halogens  are  considered 
monovalent,  unless  the  carbon  be  here  trivalent,  and  this 
does  not  seem  possible.  Tc  and  Vc  of  ethyl  iodide,  I  com- 
puted from  Ramsay  and  Shields'  surface-tension  determina- 
tions, and  this  computation  is  not  very  accurate.  Hence  I 
do  not  attach  much  weight  to  the  cohesional  evidence  of  the 
valence  of  any  of  these  compounds  of  bromine  and  iodine. 
There  are  no  indications,  however,  that  they  are  polyvalent. 
That  they  are  polyvalent  is,  however,  indicated  from  their 
action  on  light,  their  diamagnetic  properties  and  many  of 
their  chemical  properties.  Inasmuch,  however,  as  the  re- 
fraction method  is  not  very  satisfactory  for  determining 
valence,  the  question  of  the  valence  of  these  substances  must 
be  left  open,  with  the  probability  that  they  will  be  found  to  be 
polyvalent  like  chlorine.1 


1  The  fact  that  bromine  is  monovalent  in  its  elemental  state  may  account 
for  its  relative  inertness  and  is  confirmed  by  its  dissociation  at  high  tempera- 
tures, when  the  atoms  have  been  shown  to  have  but  one  active  valence.  See 
Friend:  "The  Theory  of  Valence,"  1909,  p.  18. 


262  Albert  P.  Mathews 

Fluorine  is  apparently  monovalent  in  fluorbenzene, 
since  even  with  fluorine  monovalent  the  number  of  valences 
computed  from  the  cohesion  is  still  too  small.  For  this  I 
can  give  no  reason  since  the  critical  data  of  this  substance 
seem  to  be  accurately  known.  In  methyl  fluoride  the  total 
valences  are  computed  as  9,  whereas  there  should  be  10  if 
fluorine  is  trivalent  and  8  if  it  is  monovalent.  Pascal  found 
fluorine, to  be  monovalent  by  the  magnetic  and  optical  method; 
but  Drude,  from  the  optical  behavior  of  calcium  fluoride,  be- 
lieved it  to  be  polyvalent.  The  critical  data  of  more  fluorine 
compounds  must  be  accurately  determined  before  the  cohe- 
sional  method  can  determine  the  valence  of  fluorine.  The 
chemical  behavior  of  hydrogen  fluoride  leaves  no  doubt  that 
in  it  fluorine  is  polyvalent. 

There  is  still  another  interesting  conclusion  from  this 
study :  it  appears  that  all  substances,  and  only  those  substances, 
associate,  which  are  found  by  this  method  to  contain  active, 
free  valences.  I  believe  we  may  here  have  the  explanation 
of  the  cause  of  association;  and  possibly  the  reason  why  as- 
sociating substances  dissolve  in  other  associating  liquids 
and  are  there  normal,  but  as  this  is  a  separate  problem  in 
itself,  I  shall  hope  to  return  to  it  later. 

Summary  and  Conclusion 

1.  If  the  valence  of  chlorine  be  determined  by  the  co- 
hesional  method  it  is  found  to  be  trivalent  in  its  elemental 
state  and  in  nearly  all  the  compounds  examined.     The  three 
valences  of  the  chlorine  in  these  compounds  are  not  reserve 
valences,  but  are  all  in  action  and  extending  between  the 
atoms  of  the  molecule.     Graphic  formulae  have  been  suggested 
based  on  this  fact. 

2.  This  result  is  in  harmony  with  the  determination  of 
the  valence  of  chlorine  by  the  diamagnetic   and  refraction 
method. 

3.  The  valence  of  fluorine  is  more  doubtful,  but  appears 
to  be  unity  in  fluorbenzene.     Bromine  has  unity  valence  in 

ts  elemental  form.     The  valence  of   iodine  and  bromine  in 


The  Valence  of  Chlorine  263 

their  compounds  cannot  be  definitely  determined  from  their 
cohesion  on  account  of  the  inadequacy  of  the  critical  data. 

4.  The  cohesional  method  detects  two  kinds  of  valences, 
namely,  valences  actually  extending  between  the  atoms 
and  active  in  binding  the  atoms  together;  and  valences  active 
or  open,  which  are  in  a  position  to  unite,  but  to  which  no 
atoms  are  attached.  Reserved,  or  resting,  valences  play  no 
part  as  valences  in  molecular  cohesion. 

University  of  Chicago 


THE  VALENCE  OF  OXYGEN,    SULPHUR,    NITROGEN 

AND    PHOSPHORUS    DETERMINED    FROM    THE 

MOLECULAR  COHESION 


BY   ALBERT   P.    MATHEWS 

i.  The  valence  of  oxygen 

In  my  paper  on  the  relation  of  molecular  cohesion  to 
molecular  weight  and  valence,1  in  which  the  number  of  valences 
were  computed  from  the  value  "a"  of  van  der  Waals'  equa- 
tion, I  considered  oxygen  to  be  bivalent  except  in  the  case  of 
oxygen  gas.  The  question  of  the  quadri valence  of  oxygen 
was  not  taken  up,  because  I  wished  to  get  the  main  point  of 
the  connection  of  valence  and  cohesion  well  established  be- 
fore discussing  particulars.  But  as  it  is  believed  by  many 
that  oxygen  is  at  times  quadrivalent  and  as  this  possibility 
has  such  an  important  bearing  on  theories  of  association  and 
solubility  and,  indeed,  on  the  ionizing  powers  of  water,  and 
is  also  full  of  importance  in  physiology,  it  is  interesting  to 
examine  the  oxygen  compounds  of  that  table  for  evidence 
in  favor  of  tetravalence. 

One  atom  of  oxygen  is  supposed  by  Stieglitz,  Arm- 
strong, and  Goldschmidt2  to  be  quadrivalent  in  the  esters. 
In  the  first  table,  therefore,  I  have  incorporated  the  results 
of  a  determination  from  the  molecular  cohesion  by  the  usual 
formula  :n  ==  a3/2  X  3.2  X  io5/(mol.  wt.),  of  the  total  number 
of  valences  per  molecule,  and  compared  it  with  the  number  of 
valences  computed  if  one  oxygen  is  quadrivalent.  I  have 
taken  only  those  esters  whose  critical  data  were  recently 
very  carefully  determined  by  Young.  All  of  these  esters 
associate  a  little  at  low  temperatures,  but  their  vapors  are 
normal  for  some  degrees  below  the  critical  temperature, 
except  possibly  that  of  methyl  formate. 


1  Mathews:  Jour.  Phys.  Chemv  17,  181  (1913). 

2  Zeit.  Elektrochemie,  10,  221  (1904). 


332 


Albert  P.  Mathews 


TABLE  i 


Theoretical 

•KJ                £ 

Number  of 

Substance 

Formula 

"a" 

JNO.  OI 

valences. 

valences 
det.  from 

One  oxygen 
quadrivalent 

cohesion 

Ethyl  acetate 

C4H802 

o  .  04076 

30 

29.9 

Ethyl  formate 

C3H602 

0.03122 

24 

23-9 

Ethyl  propionate 

C5H1002 

0.05088 

36 

36.0 

Methyl  acetate 

C3H602 

0.03206 

24 

24.8 

Methyl  butyrate           C5H10O2 

0.05082 

36 

35-9 

Methyl  formate 

C2H402 

0.02371 

18 

19-5 

Methyl  isobutyrate 

C5H1002 

0.04882 

36 

33-8 

Methyl  propionate 

C4H802 

0.03968 

30 

28.8 

Propyl  acetate 

C5H1002 

0.05149 

36 

36.7 

Propyl  formate 

C4H802 

o  .  04086 

30 

29.7 

From  Table  i  it  is  clear  that  the  number  of  valences 
computed  from  the  molecular  cohesion  is  very  close  to  the 
theoretical  number,  if  one  of  the  oxygen  atoms  is  quadri- 
valent. The  only  cases  in  which  fewer  valences  were  found 
were  methyl  isobutyrate  and  methyl  propionate.  In  the 
former,  the  computation  of  "a"  may  not  be  exactly  right 
as  elsewhere  pointed  out,  the  isocompounds  always  giving  a 
value  for  "a"  a  little  low  as  compared  with  the  normal.  It 
is,  of  course,  possible  that  in  them  the  oxygen  is  bivalent. 

Table  2  contains  some  other  oxygen  compounds  which 
associate  and  may  be  supposed  on  that  account  to  have 
quadrivalent  oxygen. 

In  Table  2  the  alcohols  probably  associate  somewhat 
at  the  critical  temperature  and  acetic  acid  also;  the  number  of 
valences,  given  in  the  table  as  computed,  were  computed 
with  the  normal  molecular  weight  and  they  are,  accordingly, 
too  many.  It  is  impossible  to  determine  the  total  number 
of  valences  per  molecule  by  this  method  for  these  substances 
until  the  average  molecular  weight  has  been  independently 
determined  at  the  critical  temperature.  Of  the  other  sub- 
stances: acetone,  anisol,  phenetol,  nitrobenzene,  acetic  anhy- 
dride, ethyl  diacetate  and  methyl  propyl  ketone  appear  to 
have  tetravalent  oxygen.  The  method,  however,  is  not 


The  Valence  of  Oxygen,  Etc. 


333 


TABLE  2 


Number  of 

Substance 

Formula 

"a" 

valences 
computed  ; 

No.  of  valences 
found 

one  oxygen 

quadrivalent 

Acetone 

C3H60 

0.02459 

22 

21.3 

Ethyl  alcohol 

C2H60 

0.02395 

18 

25.8  (Assoc.) 

Anisol 

C7H80 

0.05645 

40 

39-8 

Methyl  alcohol 

CH4O         0.01895 

12 

26.0  (Assoc.) 

Phenetol 

C8H10O      0.07009 

46 

48.7 

Propyl  alcohol 
Acetic  acid 

C3H80 
C2H402 

0.03250           24 
0.03504          I  8 

31.3  (Assoc.) 
34.9  (Assoc.) 

Nitrobenzene 

C6H5N02 

0.05968          38 

37-9 

Acetic  anhydride 

C4H603 

o  .  04442 

30 

29-3 

Ethyl  diacetate 

C6H1003 

0.06668*         42 

42.4 

Methyl  propyl  ketonei  C5H10O 

0-04437         34 

34-8 

m-Cresol                        !  C7H8O 

0.06254         4° 

46.0  (Assoc.) 

sufficiently  accurate  to  enable  this  conclusion  to  be  drawn 
without  reservation.  The  critical  data  of  some  of  these  sub- 
stances have  not  been  determined  with  entire  accuracy  and 
it  is  possible,  in  some,  that  a  very  small  amount  of  association 
may  occur  at  the  critical  temperature  and  such  association 
would  have  the  effect  of  making  uncertain  the  valence  de- 
termination. With  these  reservations,  however,  this  method 
undoubtedly  supports  the  view  that  oxygen  may  be  tetra- 
valent,  and  particularly  that  one  atom  is  tetravalent  in  the 
esters. 

The  method  shows  oxygen  to  be  bivalent  in  ether,  sulfur 
dioxide,  carbon  dioxide  and  one  of  the  oxygen  atoms  of  the 
esters. 

In  oxygen  gas,  carbon  monoxide  and  nitric  oxide,  NO, 
the  oxygen  is  monovalent,  if  computed  from  the  cohesion. 
The  maximum  number  of  valences  in  a  molecule  of  oxygen 
found  by  this  method  was  two.  It  must  be  confessed  that  it 
seems  unlikely  that  oxygen  is  monovalent  in  the  gaseous 
form,  but  the  critical  data  are  accurately  determined  and  if 
this  method  of  determining  valence  is  reliable,  as  it  appears 
to  be,  there  is  no  escaping  the  conclusion.  The  critical  data 
of  carbon  monoxide  should  be  redetermined,  but  from  those 


334 


Albert  P.  Mathews 


accepted  only  two  valences  can  be  found  in  the  molecule. 
Nitric  oxide  has  always  been  a  puzzle,  since  the  oxygen  is 
monovalent,  or  the  nitrogen  bivalent.  The  cohesion  shows 
that  there  are  only  two  valences,  which  again  means  that  the 
oxygen  and  nitrogen  are  monovalent.1 

From  its  cohesion,   then,   oxygen  appears  to  be  either 
monovalent,  bivalent,  or  tetravalent. 

2.  Sulfur 

Sulfur  is  generally  supposed  to  be  bivalent,  but  at  times 
to  open  up  two  or  four  residual  valences.  So  far  I  have  not 
found  any  compounds  with  bivalent  sulfur,  except  probably 
carbonyl  sulfide,  when  the  valence  is  computed  from  the 
cohesion.  All  the  sulfur  compounds  have  either  quadrivalent 
or  hexavalent  sulfur,  if  the  valence  is  determined  by  this 
method.  Even  sulfuretted  hydrogen  is  no  exception  to  this 
statement.  Table  3  contains  the  results. 
TABLE  3 — THE  VALENCE  OF  SUBSTANCES  CONTAINING  SULFUR 


Valences  permol. 

Valences  per 

Substance 

Formula.          "  n  " 

S  =  6 

S  =  4 

cohesion 

Hydrogen  sulfide 

H2S 

o  .  00890 

8 

6 

7.9 

Mercaptane 

C2H6S 

0.02497 

20 

18 

20.4 

Thiophene 

C4H4S 

6.04130 

26 

24 

32  .o(Assoc.) 

Sulfur  dioxide 

S02 

0.01349 

10 

8 

7.8 

Carbon  bisulfide 

CS2 

0.02316 

16 

12 

14.8 

Sulfuryl  chloride 

S02C12 

0.04382       1  6 

14 

14.1 

Thionyl  chloride 

SOC12 

0.03110       14 

12 

14.8 

1  A  very  interesting  fact  which  may  be  cited  in  support  of  the  view  that 
oxygen  in  these  three  gases  is  in  a  state  different  from  the  ordinary,  and,  hence, 
possibly  monovalent,  is  the  following:  Oxygen  gas  and  nitric  oxide  are  strongly 
paramagnetic,  and  carbon  monoxide  is  far  more  paramagnetic,  or  rather  far  less 
diamagnetic,  than  carbon  dioxide  which  contains  more  oxygen.  In  all  other 
compounds  oxygen  is  diamagnetic.  It  is  clear  that  the  oxygen  in  the  three 
gases  which  this  method  shows  to  contain  monovalent  oxygen  has  magnetic 
properties  different  from  oxygen  in  other  oxygen  compounds.  This  fact  has  not 
hitherto  been  explicable.  The  following  figures  showing  the  para-  or  diamag- 
netism  of  different  gases  I  have  taken  from  Auerbach's  article  on  Magnetism  in 
the  Handbuch  der  Physik,  5,  274  (1908). 

O2          NO         CO      Air    C2H4        CH4       CO2          N2O         N2  H2 

+  4.83;  +1.60;    -0.009;    *>    -0.068; -0.063;    ~°-°33!    -0.018;    -0.015;    -o.oo2(?) 


The  Valence  of  Oxygen,  Etc. 


335 


From  Table  2  it  appears  that  sulfur  is  quadrivalent  in 
sulfur  dioxide  and  sulfuryl  chloride;  hexavalent  in  sulfuretted 
hydrogen,  carbon  bisulphide,  mercaptane,  thionyl  chloride 
and  probably  in  thiophene.  It  is  probably  bivalent  in  car- 
bonyl  sulphide,  but  the  critical  data  are  uncertain.  These 
results  are  in  agreement  with  the  general  idea  of  the  valence 
of  sulfur  except  in  the  case  of  sulfuretted  hydrogen,  mer- 
captane, and  carbon  bisulfide.  Thiophene  probably  associates 
a  little  at  the  critical  temperature  so  that  the  valence  com- 
putation is  uncertain. 

j.  Nitrogen 

Nitrogen  is  generally  supposed  to  be  either  mono-, 
tri-  or  pentavalent.  The  cohesion  method  supports  this  con- 
clusion. Nitric  oxide  has  been  a  stumbling  block.  The  re- 
sults are  given  in  Table  4. 

TABLE  4 — NUMBER  OF  VALENCES   PER  MOLECULE  OF  NITROGEN 

COMPOUNDS 


Substance 

Formula 

"a" 

Number 
of  valences 
found  from 
cohesion 

Number  computed 

N  =  i 

N=3 

N  =  5 

Nitrogen 

N2 

0.0032808 

2  .0 

2 

6 

10 

Nitrous  oxide 

N2O 

0.009465 

6.2 

4 

8 

Nitric  oxide 

NO 

0.002570 

1.4 

2 

4 

Nitric  dioxide 

N02 

O.OIIIQ 

7.6 

7 

9 

Ammonia 

NH3 

o  .  00844 

13-5 

6 

8  (Assoc.) 

Methyl  amine 

CH5N 

0.01521 

17.9 

12 

14  (Assoc.) 

Dimethyl  amine 

CyHjN 

0.01922 

17-5 

18 

20 

Trimethyl  amine 

C3H9N 

0.02594 

22  .  7 

24 

26 

Diethyl  amine 

C4HUN 

0.03625 

27.9 

30 

Triethyl  amine      C6H15N 

0.05415 

39  9 

42 

Propyl  amine 

C3H9N 

0.02729 

24-5 

24 

Dipropyl  amine 

C6H15N 

0.05835 

5i-2 

52 

Aniline 

C6H7N 

0.05157 

37-2 

34 

36 

Dimethyl-0-tolui- 

dine 

C9H13N 

0.08187 

5i-2 

52 

54 

From  the  table  it  appears  that  nitrogen  in  nitrogen  gas 
is  monovalent.     It  appears  to  be  also  monovalent  in  nitrous 

and  nitric  oxide.     Two  formulas  may  be  written  for  nitrous 

\/ 
oxide  with  a  total  valence  of  six,  i.  e.,  N — O — N  or  N — N  =O. 


336  Albert  P.  Mathews 

I  think  the  former,  with  some  of  the  molecule  having  quadri- 
valent oxygen,  is  perhaps  the  more  probable.  I  have  taken 
the  highest  possible  value  of  "a"  for  nitrous  oxide.  In 
nitric  oxide  two  valences  per  molecule  are  the  most  that  can 
be  assigned  by  this  method.  This  would  mean  that  both 
elements  were  monovalent,  but  as  there  is  other  evidence 
that  oxygen  is  univalent  in  its  elemental  form,  this  formula 
is  not  entirely  improbable.  The  valence  of  nitrogen  in  nitric 
dioxide  is  quite  uncertain.  In  the  amines  there  can  be  hardly 
a  doubt  that  it  is  trivalent,  or  at  times  pentavalent  with  two 
free  valences  on  the  nitrogen.  This  is  the  case  in  ammonia 
and  methyl  amine,  both  of  which  associate.  All  of  the 
critical  data  of  the  amines  were  determined  by  Vincent  and 
Chappuis  and  I  believe  their  figures  are  uniformly  a  little  too 
low.  In  aniline  the  nitrogen  appears  to  be  pentavalent, 
but  some  association  occurs.  The  results  are  not,  then,  very 
satisfactory  for  these  compounds,  but  they  indicate  very 
clearly,  however,  that  nitrogen  is  either  monovalent,  tri- 
valent, or  pentavalent,  as  it  is  supposed  to  be. 

4.  Phosphorus 

I  have  found  but  a  single  phosphorus  compound  in  which 
the  critical  data  have  been  directly  determined,  although 
one  or  two  other  cases  were  reported  in  my  paper  on  the 
valence  of  chlorine,  in  which  the  critical  data  had  been  com- 
puted from  the  surface  tension. 

In  phosphoretted  hydrogen  the  phosphorus  is  apparently 
pentavalent,  having  two  free  valences,  "a"  is  given  by 
Leduc  and  Sacerdote  as  0.00939  and  from  this  the  valence 
of  8.6  is  computed.  Were  the  phosphorus  pentavalent  the 
total  number  of  valences  would  be  eight.  It  might  be, 
however,  that  the  phosphorus  was  heptavalent,  but  only  a 
few  of  the  molecules  had  the  two  pairs  of  reserve  valences 
open  at  the  same  instant.  In  the  chlorine  compounds  it  ap- 
peared that  the  phosphorus  was  probably  heptavalent.  I 
think  the  only  certain  conclusion  is  that  the  valence  is  greater 
than  three. 

University  of  Chicago 


THE  VALENCE  OF  THE  ARGON  GROUP  AS  DETER- 
MINED FROM  THE  MOLECULAR  COHESION 


BY   ALBERT   P.    MATHEWS 

The  valence  of  the  argon  group  of  elements  is  one  of  the 
most  interesting  problems  in  chemistry.  They  are  very 
generally  regarded  as  zero  valent,  chiefly  owing  to  the  posi- 
tion they  take  in  the  periodic  system  between  strongly  electro- 
positive and  electro-negative,  univalent  elements.  That  they 
are  monatomic  is  undoubted,  but  they  might  be  monatomic, 
like  mercury  vapor,  and  still  have  valence.  Ramsay1  made 
the  suggestion,  indeed,  that  they  combine  into  molecules 
at  other  than  ordinary  temperatures.  To  account  for  the 
atomic  weight  of  argon,  which  computed  from  the  density  is 
39.9  if  the  gas  is  monatomic,  he  suggested  that  argon  is  a 
mixture  of  many  monatomic  molecules  with  a  few  diatomic 
molecules.  The  ratios  of  the  specific  heats  as  determined  is 
1.659;  whereas  if  there  were  5  percent  of  diatomic  molecules 
it  would  be  1.648.  The  theoretical  number,  if  the  gas  is 
entirely  monatomic,  is  1.667.  After  discussing  this  possi- 
bility, however,  Ramsay  says:  ''But  on  the  whole  the  pre- 
sumption is  against  the  hypothesis  that  argon  is  a  mixture 
of  monatomic  and  diatomic  molecules." 

There  is  some  evidence  that  argon  is  not  entirely  lacking 
in  chemical  affinity.  Berthelot,2  by  the  action  of  the  electric 
discharge  on  a  mixture  of  argon  and  benzene  vapor,  or  of 
argon  and  carbon  bisulphide,  produced  a  brownish  deposit 
on  the  glass  from  which  argon  could  be  reobtained.  Ramsay,3 
in  commenting  on  the  absence  of  the  argon  lines  in  the  sun's 
spectrum,  suggests,  as  a  reason,  that  it  enters  into  combina- 
tion only  at  high  temperatures,  these  compounds  being 
endothermic;  and  he  cites4  several  observations  indicating 


1  Ramsay:  "Gases  of  the  Atmosphere,"  London,  p.  231  (1902). 

-  Berthelot:  Comptes  rendus,  120,  581,  660,  1316  (1895);  124,  113  (1897). 

3  Ramsay:  Loc.  cit.,  p.  261. 

4  Ramsay:  See  footnote,  p.  538,  to  article  by  C.  Trenton  Cooke:  Zeit. 
phys.  Chem.,  55,  537  (1906). 


338  Albert  P.  Mathews 

a  union  of  argon  with  zinc,  mercury  and  some  other  elements. 
Thus  in  a  Pliicker  tube  the  cathode  metal  disintegrates  more 
rapidly  when  argon  under  low  pressure  is  in  the  tube  than 
when  nitrogen  is  there,  and  Ramsay  interprets  this  to  mean 
that  a  volatile  compound  is  formed  under  the  influence  of  the 
intense  energy  at  the  surface  of  the  electrode  and  this  com- 
pound dissociates  again  setting  free  the  metal,  which  deposits 
on  the  glass.  Under  his  direction  C.  Trenton  Cooke1  measured 
the  vapor  tension  of  zinc,  cadmium,  sulfur,  mercury  and  some 
other  metals  at  high  temperatures  in  the  presence  of  various 
gases  and  concluded  that  the  tension  of  zinc  in  argon  was 
12  percent  above  its  tension  in  nitrogen.  Cadmium  behaved 
similarly  in  helium.  Helium  seems  to  be  in  some  kind  of  a 
union  in  fergusonite,  and  to  be  capable  of  feebly  uniting  with 
platinum.  It  may  be  recalled,  also,  that  the  solubility  of 
argon  in  water  is  greater  than  that  of  helium  and  nitrogen; 
and  this  may  be  urged  as  indicating  some  kind  of  affinity 
between  water  and  argon.  Chemically,  then,  these  gases, 
though  inert,  are  not  entirely  indifferent. 

From  their  action  on  light,2  also,  a  certain  argument  may 
be  made  for  their  possessing  valence.  Thus,  according  to 
Drude,  the  dispersion  of  light  in  the  blue  end  of  the  spectrum 
is  due  to  the  valence  electrons,  and  in  the  red  end  to  the 
vibrations  of  the  electrically  charged  atomic  groups.  If  only 
the  valence  electrons  affect  blue  light,  these  gases  must  also 
have  valence  electrons,  since  they  refract  light  like  other  gases. 

The  question  whether  these  elements  have  valence,  or 
not  can  be  put  to  a  decisive  test  through  their  molecular 
cohesions.3  There  is  no  question  that  they  possess  cohesion, 
since  they  can  all  be  liquefied.  They  behave  like  all  other 
gases  in  this  respect.  Molecular  cohesion  in  all  other  sub- 
stances examined  is  a  function  of  the  product  of  the  molecular 
weight  by  the  number  of  valences.  It  has  been  shown  for  a 


1  C.  Trenton  Cooke:  Loc.  cit.,  p.  537. 

2  Cuthbertson,  C.:  "Refractive  Indices  of  the  Elements,"  Phil.  Trans., 
204,  323  (1904). 

3  Mathews:  Jour.  Phys.  Chem.,  17,  181   (1913). 


The  Valence  of  the  Argon  Group,  Etc. 


339 


great  number  of  substances  that  M2K,  a  factor  proportional 
to  "a"  of  van  der  Waals'  equation,  is  equal,  when  expressed 
in  dynes,  to  2.98  X  io~37  (mol.  wt.  X  No.  of  valences)2/3. 
A  substance  having  cohesion  cannot,  therefore,  have  zero 
valence.  If  it  had  no  valence  it  could  have  only  gravita- 
tional attraction  between  its  monatomic  molecules,  no  cohe- 
sional  attraction.  These  gases  have  cohesion  and  they  must, 
therefore,  have  valence. 

Their  valence,  n,  can  be  calculated  from  their  critical 
data  by  the  formula:  (i)  n  =  0.0043  TC3/PC3/2  (mol.  wt.);  or, 
n  '=  a3/2  X  3.2  X  io5/(mol.  wt.);  or  (2)  n  ••--  4.21  X  io~5 
(VcTc)3/2/(rnol.  wt.).  The  first  formula,  which  is  derived 
from  the  ordinary  formula  for  computing  "a"  from  the 
critical  temperature  and  pressure,  gives  values  for  "a, " 
and  hence  for  n,  a  little  lower  than  the  second  formula  in  the 
case  of  simple  gases.  The  second  formula  computes  "a" 
from  the  surface  tension,  as  shown  in  my  former  paper.  In 
Table  i,  I  have  given  both  values  and  I  regard  the  second 
as  the  more  correct;  but  as  the  critical  density  of  not  all  the 
gases  is  known,  I  have  had  to  rely  on  the  first  formula  for  a 
comparison.  The  results  given  by  the  two  formulas  are  not 
widely  different. 

The  valence,  n,  together  with  the  critical  data1  used  in 
the  calculation  are  given  in  Table  i. 

TABLE  i — COMPUTATION  OF  THE  AVERAGE  NUMBER  OF  VALENCES 
PER  MOLECULE  FROM  THE  MOLECULAR  COHESION 


Substances 

Tc  (Abs.) 

PC 

dc 

Number  of 
valences 
by  for- 

Number of 
valences  by 
formula  2 

> 

mula  i 

Helium 

5-5° 

2.75 

0.065 

0.04 

0.07 

Helium 

8.0 

2.75 

0.065 

0.  12 

O.  12 

Neon 

61.1 

29 

— 

0.32 

— 

Argon 

150-56 

48 

0.509 

I  .  12 

i-35 

Krypton 

210.5.3 

54-3 

— 

1.23 

— 

Xenon 

289.6 

58.2            I-I55          i-8° 

i-95 

1  In  my  preliminary  paper,  Science,  N.  S.,  36,  6  (1912),  in  Table  I  a 
mistake  occurred  in  the  computation  of  helium.  The  value  2.90  is  wrong. 
The  critical  density  was  taken  as  0.015  instead  of  0.065. 


340  Albert  P.  Mathews 

Before  discussing  these  results  a  word  may  be  said  about 
the  reliability  of  the  critical  data.  Those  of  argon  and  xenon 
are  perhaps  the  most  certain;  krypton,  neon  and  helium 
follow  in  the  order  named,  helium  being  least  certain.  Onnes1 
gives  5.5°  absolute  as  the  critical  temperature  of  helium, 
but  as  this  makes  helium  quite  aberrant  in  several  particulars,2 
I  have  also  computed  the  valence  assuming  the  critical  tem- 
perature to  be  8°  as  suggested  by  Dewar.3  The  critical  data 
of  neon  are  somewhat  uncertain,  due  in  part  to  the  very  low 
critical  temperature  and  in  part  to  the  great  difficulty  in 
separating  the  gas  completely  from  helium.  A  little  im- 
purity of  the  latter  gas  would  have  the  effect  of  making  Pc 
too  high. 

It  is  clear, from  the  table  that  all  of  these  gases  possess 
valence.  They  are  not  zero  valent  as  they  are  supposed  by 
many  to  be.  Furthermore,  the  average  number  of  valences 
per  molecule  is  in  no  case  an  exact  integer,  although  in  argon 
and  xenon  it  is  not  far  from  a  whole  number.  Since  these 
gases  have  their  critical  data  most  accurately  determined 
I  at  first  supposed,  as  I  published  in  my  preliminary  paper, 
that  argon  was  univalent,  but  slightly  associated  into  di- 
atomic molecules,  thus  bringing  the  average  number  of 
valences  per  molecule  a  little  high;  and  that  xenon  was  di- 
valent. I  attributed  the  deviation  of  the  other  gases  from 
uni valency,  to  the  inaccuracy  of  the  data.  A  careful  ex- 
amination of  all  the  facts,  however,  has  led  me  to  abandon 
this  explanation  for  what  seems  to  me  to  be  a  better  one, 
since  it  explains  all  the  facts. 

In  the  first  place,  I  have  not  been  willing  to  abandon  the 
idea  that  valences  are  indivisible.  If  we  assume,  as  Lodge4 
suggests,  that  some  of  the  lines  of  force  from  each  valence 
attach  themselves  to  several  atoms,  or  even  wander  outside 

1  Onnes:  Proc.  Amsterdam  Acad.  Sci.,  13,  noo  (1-911). 

2  Rankin:  "On  a  Relation   between  Viscosity    and    Atomic    Weight   of 
Inert  Gases,"  Phil.  Mag.,  [6]  21,  45  (1911). 

3  Dewar:  Article   "Liquid   Gases,"    Encyclopaedia   Britannica,    16,    749, 
nthed. 

4  Lodge:  Nature,  70,  176  (1904). 


The  Valence  of  the  Argon  Group,  Etc.  341 

the  molecule,  and  thus  split  the  valence  up;  or  that  there  are 
partial  valences  in  the  sense  of  Kauffmann,1  it  seems  to  me 
that  we  might  as  well  abandon  the  whole  valence  idea.  It 
entirely  loses  its  usefulness.  Again  our  structural  formulas 
become  so  indefinite,  if  the  valences  are  regarded  as  split  up, 
as  to  be  nearly  useless.  The  explanation  which  I  sought 
was  one  which  would  explain  why  we  appear  to  have  frac- 
tional valences  in  this  case,  but  really  do  not  have  them. 
That  my  first  explanation  was  wrong,  was  indicated  by  the 
uniformity  with  which  the  valence  increases  from  helium  to 
xenon.  The  deviation,  too,  from  uni valency  in  the  case  of 
neon  is  so  great  that  it  lies  outside  the  limits  of  error.  The 
critical  pressure  would  need  to  be  14  atmospheres  instead  of 
that  recorded  of  29  atmospheres,  in  order  that  neon  should 
have  one  valence  to  each  molecule.  The  uncertainty  of  the 
critical  pressure  is  far  less  than  this. 

I  believe  the  reason  that  the  average  number  of  valences 
is  a  fraction  in  these  gases  is  as  follows:  All  of  them  are  in 
reality  zero  valent,  so  fas  ar  their  chief  valences  are  concerned, 
but  like  many,  if  not  all,  other  elements,  they  have  the  power 
of  opening  up  two  residual  valences.  By  their  residual 
valences,  therefore,  they  are  all  bivalent.  These  two  valences, 
like  most,  or  all,  other  residual  valences,  are  of  opposite 
electrical  sign,  one  being  positive,  the  other  negative.  Not 
all  the  atoms  have  these  residual  valences  open  at  the  same 
instant,  but  always  some  of  the  atoms  have  them  closed.  The 
molecular  cohesion,  as  I  have  already  pointed  out,  is  not 
influenced  by  these  valences  when  they  are  in  a  closed  or 
reserve  state,  or,  we  might  say,  withdrawn  within  the  atom; 
it  is  only  affected  by  the  valences  actually  extending  between 
atoms,  or  open  and  in  a  state  in  which  they  may  combine. 
In  xenon  nearly  all  the  atoms,  or  at  any  rate,  90  percent  of 
them,  have  the  valences  open,  and  the  average  valence  per 
atom,  or  molecule,  is,  therefore,  1.80-1.95;  in  krypton  about 
65  percent  of  the  atom  have  open  valences,  and  35  percent 
are  closed,  so  that  the  average  valence  is  about  1.30;  in  argon, 

1  Kauffmann:  Ber.  chem.  Ges.  Berlin,  41,  4404  (1908). 


342  Albert  P.  Mathews 

about  60  percent  are  open  and  40  percent  are  closed,  the 
average  valence  being  about  1.20;  in  neon,  16  percent  are 
open  and  84  percent  are  closed,  the  average  valence  being 
about  0.32;  and  in  helium  only  about  5  percent  of  the  valences 
are  open,  95  percent  being  closed,  giving  an  average  valence 
of  o.io.  This  explains,  then,  why  the  elements  appear  zero 
valent  in  the  periodic  table,  since  they  are  zero  valent  as  far 
as  their  chief  valences  are  concerned;  why,  nevertheless,  they 
appear  to  have  some  weak  chemical  affinity,  and  cohesion; 
why  they  refract  and  disperse  light;  and  also  why  the  average 
valence  is  fractional  rather  than  being  a  whole  number. 

It  also  explains  more  than  this.  It  enables  us  to  under- 
stand the  easy  dissociation  of  the  molecules  into  atoms. 
Unlike  atoms  that  are  bound  together  into  molecules  by  their 
chief  valences,  no  electrical  stresses  are  set  up  in  the  argon 
elements  when  dissociation  into  atoms  occurs,  because  each 
atom  having  a  positive  and  a  negative  valence  becomes  at 
once  electrically  neutral.  It  is  well  known  that  compounds 
formed  from  residual  valences  partake  of  the  nature  of  molec- 
ular compounds  and  break  up  very  easily.  Neither  their 
union,  nor  their  dissociation,  involves  much,  if  any,  energy 
exchange.  Such  compounds  are  often  called,  indeed,  molec- 
ular compounds.  A  double  bond  of  this  kind  is  always  a 
weak  bond  in  any  molecule,  which  easily  breaks  where  the 
double  bond  is.  Were  they  univalent  their  dissociation  into 
atoms  would  be  very  hard  to  understand. 

I  suppose  we  may  picture  the  opening  of  these  residual 
valences  in  the  manner  suggested  by  Sir  J.  J.  Thomson,  as 
being  due  to  a  rearrangement  of  the  electrons  within  the 
atom  so  that  an  excess  of  negative  electricity  is  temporarily 
produced  in  one  spot,  and  of  positive  at  another  spot  on  the 
surface  of  the  atom.  These  excesses  are  the  valences. 

In  closing,  it  is  not  without  interest  to  compare  the 
valence  numbers  computed  above  from  the  cohesion,  with  the 
refractivity  as  determined  by  Cuthbertson.1  Their  re- 
fractivities  are  in  the  proportion  i,  2,  8,  12  and  19. 

1  Cuthbertson,  C.:  Phil.  Trans.,  204,  323  (1905). 


The  Valence  of  the  Argon  Group,  Etc. 


343 


Refract!  vity  (/*  —  i)io6 

Ratio 

Valence 

Ratio 

Helium 
Neon 
Argon 
Krypton 
Xenon 

36-3 
68.7 
284 

425 
689 

I 
1.9 
7-82 

ii.  7 
18.98 

0.  I 
0.32 

I  .  12 
I.  80 

I 

3-2 

II.  2 

I2.3 

18.0 

There  is  a  general  similarity,  but  not  an  identity. 

The  principal  facts  and  conclusions  of  the  paper  are: 
The  molecular  cohesion,  confirming  other  properties,  shows 
that  the  argon  group  of  elements  have  valence.  A  com- 
putation of  the  average  number  of  valences  per  molecule 
from  the  molecular  cohesion  gave  the  following  results: 
He,  o.i;  Ne,  0.32;  Ar,  1.12;  Kr,  1.23;  Xe,  1.80.  The  valences 
are  apparently  fractional,  and  not  whole  numbers.  The 
conclusion  is  that  these  elements  are  all  zero  valent,  as  far 
as  their  chief  valences  go,  but  each  is  divalent  in  its  residual 
valences.  At  any  one  instant  of  time  only  a  certain  pro- 
portion of  the  atoms,  varying  in  the  different  gases,  have  their 
residual  valences  open,  consequently  the  average  number  of 
valences  actually  open,  or  active,  per  molecule  is  less  than  two. 
One  residual  valence  is  positive,  the  other  negative;  and 
hence  the  combining  power  of  the  atoms  is  very  weak,  since 
on  dissociation  an  electrically  neutral  atom  is  formed,  by  the 
saturation  within  the  atom  of  the  oppositely  charged  valences. 
This  explanation  enables  us  to  understand,  also,  why  there 
is  a  progressive  increase  in  solubility  of  these  gases  in  water 
from  helium  to  xenon  if  solution  be  a  process  involving  the 
union  of  solvent  and  solute  through  their  residual  valences. 

University  of  Chicago 


A  NOTE  ON  THE  STRUCTURE  OF  ACETYLENE 


BY  ALBERT   P.    MATHEWS 

From  a  study  of  the  volume  of  liquid  acetylene,  Macintosh1 
concluded  that  acetylene  was  in  reality  acetylidene  since  one 
of  the  carbon  atoms  seemed  to  have  the  volume  of  bivalent 
carbon.  He  supported  this  contention  also  by  various  chem- 
ical arguments.  On  the  other  hand,  Nef,2  while  showing 
that  the  halogen  substitution  products  were  in  reality  acetyl- 
idene compounds,  believed  that  acetylene  was  acetylene 
and  not  acetylidene,  because  it  was  chemically  and  physiolog- 
ically so  inert.  Nef's  pupil,  Lawrie,3  confirmed  the  acetylidene 
nature  of  the  bromine  and  iodine  substitution  products. 

Although  it  is  improbable,  for  the  reasons  stated  by  Nef, 
that  acetylene  is  acetylidene,  the  matter  may  be  definitely 
settled  by  my  method  of4  determining  the  number  of  valences 
in  the  molecule  from  the  molecular  cohesion.  If  it  is  acetylene 
there  should  be  ten  valences;  if  acetylidene,  there  should  be 
eight,  since  acetylene  does  not  associate  and  one  carbon  atom 
would  be  bivalent. 

The  most  recent  determination  of  the  critical  data  of 
acetylene  by  Cardoso  and  Baume  gives  Tc,  35.5°  C;  and  Pc, 
61.6  atmospheres.  From  these  figures  the  value  of  "a"  of 
van  der  Waals'  equation  calculated  by  the  formula:  a  = 
27Tc2/64  X  2732  X  Pc,  is  0.008745.  Computing  the  number  of 
valences,  n  from  "a"  by  the  formula:  n  =  a3/2  X  3.2  X 


1  Macintosh:  "The  Physical  Properties  of  Liquid  and  Solid  Acetylene," 
Jour.  Phys.  Chem.,  n,  315  (1907). 

2  Nef:  "Ueber  das  zweiwertige  Kohlenstoffatom,"  Liebig's  Ann.,  298,  332 
(1897)- 

3  Lawrie:  "Constitution  of  Acetylidene  Compounds,"  Am.  Chem.  Jour., 
36,  487-510  (1906). 

4  Mathews:    "The  Relation  of  the  Value  'a   of  van  der  Waals'  Equation 
to  Molecular  Weight  and  the  Number  of  Valences  of  the  Molecule,"  Jour.  Phys. 
Chem.,  17,  181  (1913)- 


A  Note  on  the  Structure  of  Acetylene  321 

io5/(Mol.  Wt),  we  obtain  the  value  10.06  for  n.  There  are, 
therefore,  ten  valences  in  the  molecule  of  acetylene;  accordingly 
each  carbon  has  four,  each  hydrogen  one. 

Acetylene  is,  therefore,  acetylene,  as  it  is  ordinarily  written, 
and  not  acetylidene. 

University  of  Chicago 


DO  MOLECULES  ATTRACT  COHESIVELY  INVERSELY 
AS  THE  SQUARE  OF  THE  DISTANCE? 


BY  ALBERT  p.  MATHEWS 

In  a  very  interesting  and  valuable  recent  paper  in  this 
journal  by  Mills,1  the  conclusion  was  drawn  that  the  cohesional 
attraction  of  molecules  varied  inversely  as  the  square  of  the 
distance.  Besides  this  conclusion,  which  was  founded  on  the 
interesting  discovery  that  the  internal  latent  heat  of  vaporiza- 
tion divided  by  the  difference  of  the  cube  roots  of  the  densities 
of  the  liquid  and  vapor  was  a  constant,  a  most  valuable  part 
of  the  paper  was  the  reopening  of  the  question  whether  the 
field  of  molecular  attraction  is  delimited  by  the  surrounding 
molecules,  or  whether  it  owes  its  small  size  to  the  very  rapid 
decrease  of  the  attraction  with  the  distance.  This  question 
raised  a  century  ago  by  Laplace,2  was  answered  by  him 
in  the  latter  sense  without  any  convincing  reason  for  his 
conclusion,  and  has  not  been  reopened  since,  the  opinion 
being  almost  universal  that  the  shortness  of  the  radius  of 
action  is  due  to  the  attraction  diminishing  with  the  distance 
at  a  rate  far  more  rapid  than  the  square;  the  fourth,  fifth, 
seventh  and  even  higher  powers  having  been  suggested. 
In  thus  reopening  the  question  Mills  has  rendered  a  valuable 
service.  That  his  conclusion  is  correct,  that  the  molecular 
field  is  delimited  by  the  surrounding  molecules,  is  clearly 
indicated  by  Einstein's3  calculation  of  the  radius  of  action, 
showing  that  the  radius  is  proportional  to  the  distance  be- 
tween the  molecular  centers.  The  conclusion  that  the  at- 
traction is  inversely  as  the  square  of  the  distance,  however, 
I  believe  to  be  erroneous  for  the  reasons  which  will  be  pre- 
sented in  this  paper. 


1  Mills:  Jour.  Phys.  Chem.,  15,  417  (1911). 

a  Laplace:  "Traite"  de  me"canique  celeste,"  Supp.  an  Livre  10,  p.  351. 

3  Einstein:  Drude's  Ann.,  34,  165  (1911). 


Do  Molecules  Attract,  Etc.  521 

Mills1  discovered  the  empirical  relationship  that  the 
quotient  of  the  internal  latent  heat  of  vaporization  divided 
by  the  difference  of  the  cube  roots  of  the  densities  of  the 
liquid  and  vapor  was  a  constant,  except  in  the  neighborhood 
of  the  critical  temperature.  If  I/  is  the  total  latent  heat, 
and  E  is  the  part  of  it  used  in  doing  external  work,  then 
IY  -  -  E  would  be  the  part  of  the  heat  used  in  doing  internal 
work.  He  found  that  (L  -  -  E)/(^/3  -  -  D1/3)  =  /*' '.  He 
assumed  that  this  internal  heat  was  all  used  in  overcoming 
molecular  cohesion,  and  he  ascribed  the  fall  of  the^constant 
near  the  critical  temperature  to  the  inaccuracy  of^the  data. 
He  then  reasoned  that  since  for  u//3  —  D^/3  the  expression 
i/V|/3  --  i/V^/3  might  be  substituted,  the  molecules  must 
attract  each  other  inversely  as  the  square  of  the  distance; 
since  it  is  only  on  such  a  supposition  that  the  difference  in 
potential  energy  of  the  molecules  in  the  liquid  and  the  vapor 
can  be  given  by  an  expression  of  this  kind.  The  similarity 
of  his  expression:  I,  --  E  -=  /(i/V;/3  --  i/V^/3)  to  Helm- 
hoi  tz's  formula  for  the  heat  given  off  by  the  contraction  of 
the  sun  seemed  significant,  the  Helmholtz  formula  being 
W  ==  3/5M2K2(i/R--  i/CR).  From  this  similarity  Mills 
reasoned  that  molecular  attraction,  like  gravitational,  must 
follow  the  inverse  square  law.  Since  it  is  impossible  that 
molecules  should  attract  each  other  cohesively  according  to 
this  law,  if  the  cohesional  attraction  penetrated  matter,  he 
concluded  that  Cohesion  did  not  penetrate  matter,  but  was 
delimited  by  the  surrounding  molecules. 

There  is,  however,  another  relationship  expressing  the 
latent  heat  consumed  in  overcoming  molecular  cohesion  or 
the  internal  pressure,  which  has  been  given  by  van  der  Waals 
and  is  derived  from  his  expression  for  cohesive  pressure  of 
a/V2.  This  relationship  is:  Iv  —  E  =  a(i/V,  —  i/VJ,2  where 

1  Mills:  Jour.  Phys.  Chem.,  15,  417  (1911);  Comptes  rendus,  153,   193 
(1911);  Phil.  Mag.,  [6]  22,  84  (191;!);  [6]  23,  484  (1912). 

2  This  formula  should,  in  my  opinion,  be  written:  L  -—  E  —  X  =  a  (i/Vj- 
i/Vy)  where  X  represents  heat  used  in  any  other  internal  work  than  the  separa- 
tion of  the  molecules.     See  van  der  Waals:     "Condensation  of  Gases,"  Encyclo. 
Britannica,  xi  edition.     Also  .Sutherland:  Phil.  Mag.,  [5]  22,  83  (1886). 


522 


Albert  P.  Mathews 


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Do  Molecules  Attract,  Etc. 


523 


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Benzene 

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524  Albert  P.  Mathews 

"a"  is  van  der  Waals'  constant.  According  to  Sutherland1 
the  latter  expression  indicates  that  the  attraction  of  the  mole- 
cules is  inversely  as  the  fourth  power;  whereas  Mills  has 
interpreted  the  former  as  meaning  that  it  is  inversely  as  the 
square. 

To  show  how  constant  Mills'  constant  is,  I  have  given, 
in  Table  i,  the  results  of  the  calculations  by  his  formula  of  a 
number  of  substances  from  Young's  data.  The  figures  re- 
present ergs  for  gram  molecular  quantities.  It  will  be  seen 
that  the  constancy  is  good  for  a  considerable  range  of  tem- 
perature, but  that  in  all  cases  there  is  a  more  or  less  pro- 
nounced drop  close  to  the  critical  temperature,  and  in  some, 
as  in  ether  and  ethyl  acetate,  there  is  a  pretty  steady  fall 
in  the  constant  throughout.  The  fall  near  the  critical  tem- 
perature might  be  ascribed  to  errors  of  observation,  or  calcula- 
tion. There  is  no  doubt,  therefore,  that  for  most  substances 
the  expression  (L  --  E)/(3v/^1  -  8VDW)  closely  approximates 
a  constant  except  near  the  critical  temperature,  as  Mills  has 
pointed  out. 

The  conclusion  that  this  relationship  shows  that  the 
molecules  attract  inversely  as  the  square  of  the  distance  is, 
I  believe,  sound,  if  the  premise  is  correct.  The  premise,  or 
assumption,  is  that  the  internal  latent  heat  of  vaporization, 
or  Iy  —  E,  represents  only  the  work  done  in  separating  the 
molecules  against  their  molecular  cohesion.  While  Mills1 
states  in  a  recent  paper  that  not  all  the  internal  heat  may  be 
used  in  doing  this  work,  and  attempts  to  show  that  this  is 
not  incompatible  with  this  conclusion,  the  conclusion  never- 
theless depends  on  the  assumption  that  it  is  so  used  and  that 
there  is  no  change  in  the  internal  energy  of  the  molecules  on 
passing  from  the  liquid  to  the  vapor.  It  is  clear  that  if  this 
premise  be  not  true,  then  the  conclusion  does  not  follow. 

This  premise  I  believe  to  be  certainly  erroneous.  It 
could  only  be  true  if  the  molecules  remained  of  the  same 


1  Mills:  Phil.  Mag.,  [6]  22,  97  (1911);   23,  499  (1912). 


Do  Molecules  Attract,  Etc.  525 

size  in  liquid  and  vapor,  or  do  not  in  other  ways  gain  energy.1 
I  believe  the  internal  latent  heat  of  vaporization  consists  of 
at  least  three  parts,  not  two  as  is  often  stated,  these  three 
parts  are :  (i)  the  heat  consumed  in  expanding  against  external 
pressure,  or  E;  (2),  the  heat  consumed  in  overcoming  molec- 
ular cohesion,  or  A;  (3),  heat  consumed  in  increasing  internal 
molecular  potential  energy  by  expanding  the  molecule,  or 
increasing  its  energy  of  rotation,  or  I.  This  last  factor  is 
often  overlooked.  If  L  is  the  total  latent  heat  of  vaporiza- 
tion the  expression  should  be :  L  —  E  —  I  ==  A.  And  if  mole- 
cules attract  inversely  as  the  square  of  the  distance  we  should 
have  (I,  —  E  —  I)/(V^—  VDJ  -  /. 

There  are  two  principal  reasons  why  it  cannot  be  assumed 
that  all  the  internal  latent  heat  of  vaporization  goes  to  in- 
creasing the  potential  energy  by  separating  the  molecules 
against  the  force  of  their  molecular  cohesions.  The  first  of 
these  reasons  is  that  the  value  "b,"  of  van  der  Waals'  equa- 
tion, has  to  be  taken  larger  in  the  vapor  than  in  the  liquid 
for  some  distance  below  the  critical  point.  And  there  are 
good  reasons  for  thinking  that  "6"  represents  the  real  volume 
of  the  molecules.  The  second  reason  is  the  value  a/V2  re- 
presenting cohesion  in  van  der  Waals'  equation.  A  third 
reason  has  been  given  by  Tyrer. 

To  show  that  the  molecules  actually  do  expand  in  passing 
from  the  liquid  to  the  vapor,  I  have  calculated  the  value  of 
"6"  for  pentane,  and  benzene  using  Young's  data.  I  have 
also  calculated  several  others  of  his  substances,  but  as  the 
result  is  similar  in  them  to  that  in  these  two,  I  give  only  the 
latter  in  Table  2,  which  shows  the  value  of  b  in  cc  in  the  liquid 
and  vapor  for  gram  molecular  quantities  b  V  -  RT/- 
(P  +  a/V2).2 

1  A  similar  objection  to  Mills'  conclusion  has  been  raised  by  Professor 
Tyrer:  Phil.  Mag.,  [6]  23,  112  (1912). 

2  Since  sending  this  paper  to  the  publisher  I  have  found  that  the  value  of 
"a"  is  larger  than  assumed  here.     This  change  requires  be  and  b-v  both  to  be 
larger.     At  150°  bv  should  be  about  127  cc  and  at  40°  only  — 14.     The  relation 
between  be  and  bv  is  not  greatly  changed,  but  the  difference  between  them 
becomes  greater. 


526 


Albert  P.  Mathews 


TABLE  2 
Pentane 


t 

*, 

bv 

Vv 

P(At) 

a/MJ 

40° 

100.6 

—140 

21,420 

I-I5 

0.04 

100 

106.5 

-  64.  i 

4,428.OO 

5.80 

I  .09 

150 

114.6 

79-9 

1,512.60 

15-54 

8.72 

180 

124.2 

140.3 

790.05 

25.46 

31.96 

190 

130.8 

I5I-9 

567-36 

29.61 

6  1  .90 

195 

137.2 

155-2 

447-5 

3I-9I 

99-55 

197 

H4-5 

153-3 

359-iQ 

32.90 

I54-70 

197.2 

149.4 

149.4 

309-94 

33-03 

2°7-5o  (critical) 

Benzene 


t 

*, 

M 

vv 

80° 

82.3 

70 

28,570 

1  20 

84.6 

-170 

10,160 

1  60 

87.4 

22 

5,428 

2OO 

90.8 

52 

2,200 

240 

96.2 

89 

1,093 

260 

100.5 

II0.3 

751-7 

270 

103.6 

120 

606 

280 

108.2 

127 

470 

288.5 

123.8 

123.8 

256.2 

Table  2  shows  that,  in  pentane,  bv  is  larger  than  b^  from  the 
critical  temperature  to  about  160°.  Below  this  point  vv 
falls  rapidly  and  apparently  soon  becomes  negative.  The 
reason  for  this  apparent  fall  is  undoubtedly  the  association, 
or  quasi- association,  occurring  in  the  vapor  as  the  temperature 
falls,  as  van  der  Waals  suggests,  the  result  being  that  the 
number  of  the  molecules  in  the  space  does  not  remain  con- 
stant and  hence  R  does  not  remain  constant.  The  effect 
of  reducing  R  to  its  real  value,  were  we  able  to  correct  for 
the  association,  would  be  to  make  bv  larger.  In  benzene 
bv  falls  below  bl  sooner  than  in  pentane,  from  which  we  may 
infer  that  the  association  in  benzene  is  a  little  larger  than  in 
pentane.  The  apparently  negative  value  of  bv  is  found 
closer  to  the  critical  temperature  in  the  esters  which  are 
known  to  associate  slightly.  Since  association  produces  an 


Do  Molecules  Attract,  Etc. 


527 


apparent  decrease  in  bv,  it  is  practically  certain  that  the 
differences  between  b^  and  bv  are  actually  larger  than  those 
indicated.  The  main  fact  is  then  established  that  bv  is  actually 
larger  than  bl  for  some  degrees  below  the  critical  point  in  spite  of 
the  association  which  tends  to  mask  the  actual  molecular  ex- 
pansion and  which,  at  lower  temperatures,  conceals  it  en- 
tirely. 

It  will  be  seen,  also,  that,  as  one  would  expect,  bv  actually 
decreases  close  to  the  critical  temperature,  owing  to  the  com- 
pression of  the  molecules  due  to  the  great  increase  in  internal 
and  external  pressure.  This  increase  of  pressure  (P  +  a/V2) 
is  indicated  in  Table  2  in  the  case  of  pentane,  the  pressures 
being  given  in  atmospheres  per  sq.  cm. 

It  is  of  interest,  in  this  connection,  to  compute  what  is 
possibly  the  real  value  of  bv,  making  van  der  Waals'  assumption 
that  in  the  vapor,  at  low  temperatures,  bv  is  equal  to  2&r 
Supposing  that  this  is  the  case  at  absolute  zero  we  may  write 
the  rectilinear  diameter  formula :  6t  +  b^  =  bc  ((3TC  +  T)/2TC). 
This  assumes  that  at  absolute  zero  the  molecules  are  so  com- 
pressed that  in  the  solid  their  volume  is  one-half  of  what  it 
would  be  in  the  vapor  at  the  same  temperature,  and  that  the 
volume  of  the  vapor  molecules  at  absolute  zero  is  that  of  bc. 

+  T)/2TC))-&1. 


bc  is  very  nearly  Vc/2 .     Table  3  bv 


TABLE  3 
Pentane 


t 

6, 

bv  (cal) 

bv  (taken  from  Table 

2) 

40° 

100.6 

173.2 

—140 

100 

106.5 

176.9 

-7—64.1 

150 

114.6 

176.7 

79-9 

1  80 

124.3 

171.9 

140.3 

190 

130.8 

166.8 

151-9 

195 

137.2 

161.3 

155-2 

197 

H4-5 

154-3 

153-3 

197.2 

149.4 

149.4 

149.4 

The  parabola  represented  by  these  figures  is  given  in 
Fig.   i.     If  there  is  any  association  in  the  liquid  the  effect 


528 


Albert  P.  Mathews 


of.  correcting  for  it  would  be  to  reduce  the  value  of  bv  and 
increase  bl  and  so  to  make  the  parabola  flatter.  I  have 
computed  bl  assuming  that  there  is  no  association  in  the 
liquid.  The  increase  of  bv  with  the  temperature  is  seen  to  be 
very  slight.  From  absolute  zero  to  the  maximum  value  at 
100°  the  increase  is  at  the  rate  of  0.074  cc  per  degree  for  gram 
mol  quantities.  On  the  other  hand  "6"  changes  markedly 
with  the  pressure. 

There  are  several  reasons  for  believing  that  "b"  is  the 
real  volume  of  the  molecules  and  not  four  times  the  volume 
as  was  originally  suggested.  One  is  that  "b"  at  the  critical 


Fig.  i — Volumes  of  molecules  (b  for  gram  mol  quantities  in  cc.)  for  pentane. 
bl  calculated  from  formula  b1  =  V1  —  RT/(P  +  a/Vf )  assuming  no  asso- 
ciation; bv  calculated  by  formula:  bv  =  bc((sTc  +  T)/2TC))  b^,  bvf  apparent 
volume  of  bv  by  formula:  &„'  =  Vv  RT/(P  +  a/Vj)  assuming  no  association. 

temperature  is  very  nearly  Vc/2  and  this  is  just  twice  the 
volume  at  absolute  zero.  It  is  unlikely  that  the  molecules 
do  not  expand  in  passing  from  absolute  zero  to  the  critical 
temperature,  since  at  the  former  temperature  they  are  under 
a  pressure  of  3572  atmospheres  in  pentane,  whereas  at  the 
critical  temperature  the  pressure  is  only  240  atmospheres. 
It  would  take  very  little  separation  of  the  atoms  to  double 
the  volume. 

The  latent  heat  shows,  also,  that  heat  is  absorbed  by  the 
molecule  roughly  proportional  to  the  number  of  atoms  in 
the  molecule.  This  would  mean  that  the  atoms  vibrated 
(or  expanded)  and  they  must  hence  take  up  more  space  as  the 
vigor  of  vibration  increases.  This  would  seem  to  be  sufficient 


Do  Molecules  Attract,  Etc.  529 

to  account  for  doubling  the  volume  of  b  between  o°  Abs.  and 
Tc.  Van  der  Waals1  himself  only  assumed  the  constancy 
of  the  molecular  volume  "6"  for  simplicity,  an'd  has  now 
definitely  adopted  the  idea  of  a  change  in  volume  of  the 
molecules.  He  has  obtained,  by  making  certain  assumptions, 
the  following  expression  for  the  change  of  ilb, "  the  molecular 
volume:  (b  —  b0)/(V  -  -  b)  =  =  i  -  -  (b  --  b0Y/(bg  —  b0}\  In 
this  equation  bg  and  b0  are  the  limiting  values  of  b ;  bg  at  low 
vapor  pressures,  and  b0  under  high  pressure;  the  actual  value 
under  any  temperature  and  pressure  is  "b."  Van  der  Waals 
assumes  that  in  liquids  at  low  temperatures,  bg  ==  2b0.  Both 
probability  and  direct  observation  lead,  therefore,  to  the 
conclusion  that  the  molecules  expand  on  passing  from  the 
liquid  to  the  vapor  state. 

It  is  clear  that  if  the  molecules  do  thus  expand  against- 
the  great  force  of  atomic  affinity,  or  intra-molecular  cohesion, 
some  heat  must  be  absorbed.  The  quantity  thus  absorbed 
will  probably  be  greatest  at  low  temperatures,  where  there  is  a 
maximum  difference  in  cohesive  pressure  between  the  liquid 
and  the  vapor,  and  will  diminish  rapidly  near  the  critical 
temperature,  since  the  volumes  of  the  molecules  in  the  two 
states  approach  each  other  and  become  equal  at  the  critical 
temperature.  As  we  near  the  critical  temperature,  therefore, 
the  value  of  I  will  become  very  small,  and  the  equation  L  - 
E  ==  A  will  become  very  nearly  true. 

The  second  reason  why  the  internal  latent  heat  of 
vaporization  can  not  be  assumed  to  go  altogether  to  increas- 
ing the  distance  between  the  molecules  is  the  fact  that  the 
internal  pressure,  the  cohesive  pressure,  is  inversely  pro- 
portional to  the  square  of  the  volume.  For,  assuming  as  be- 
fore that  all  the  latent  heat  goes  toward  separating  the  mole- 
cules, if  a/V2  is  the  cohesive  pressure  per  unit  surface  then  the 
cohesive  energy  in  the  liquid  will  be  a/V^  and  in  the  vapor, 
a/V,,;  and  the  difference  in  their  cohesive  energies  will  be 


1  Van  der  Waals:    "The  Liquid  State  and  the  Equation  of  Condition," 
Proc.  Roy.  Acad.  Sci.  Amsterdam  (English  Translation),  6,  123  ,(1903)- 


530  Albert  P.  Mathews 

a(i/V1  --  i/VJ.  By  our  assumption  this  difference  in  energy 
must  be  equal  to  L  -  -  E.  Hence  (L  -  -  E)/(i/V1  -  -  i/Vw) 
must  equal  "a."  We  come,  therefore,  to  an  expression 
different  from  Mills  and  one  incompatible  with  it.  Since 
it  is  certain  that  the  cohesive  pressure  varies  at  least  ap- 
proximately inversely  as  the  square  of  the  volume  this  ex- 
pression must  be  the  correct  expression,  if  Iy  —  E  represents 
only  heat  consumed  in  overcoming  cohesion.  As  a  matter  of 
fact  (Iv  —  E)/(i/Ve  —  i/Vv)  does  not  equal  a  constant,  hence 
our  assumption  must  be  wrong.  But  if  the  assumption  is 
wrong  then  the  fact  that  (L  —  E)/(i/V'/3  —  i/V^3)  happens 
to  equal  a  constant  can  not  be  adduced  as  evidence  that 
molecules  attract  inversely  as  the  square  of  the  distance. 

I  think  therefore,  that  Mills'  empirical  expression, 
I,  —  g  =  ^'(i/V'/8  --  Vj,7*)  does  not  mean,  as  he  supposed, 
that  the  work  done  in  overcoming  molecular  cohesion  from 
the  volume  V1  to  the  volume  Vv  was  equal  to  /(i/V^3  - 
i/V^3),  but  that  the  total  internal  latent  heat,  i.  e.,  that  used 
in  overcoming  molecular  cohesion  as  well  as  that  absorbed 
in  the  expansion  of  the  molecules,  or  in  doing  other  work  is 
equal  to  this  expression. 

That  Mills'  expression,  /(i/V^1  -  i/V^3),  does  not 
represent  the  work  done  in  overcoming  molecular  cohesion 
may  be  shown,  also,  if  the  attempt  is  made  to  deduce  the 
formula  on  this  basis,*~assuming  the  attraction  to  vary  in- 
versely as  the  square  of  the  distance.  A  value  is  obtained 
for  //  widely^different  from  that  found.  Mills  realized  this 
difficulty  and  tried  to  avoid  it  by  assuming  that  the  law  that 
matter  attracted  itself  as  the  product  of  the  masses  was 
incorrect. 

^ll  will  make  the  simplest  possible  assumptions.  If  the 
molecules  are  assumed  to  be  cubical  in  shape,  to  lie  a  mean 
distance  apart  and  the  lines  of  attractive  force  to  run  per- 
pendicularly from*each  face  of  the  cube  in  three  directions 
of  space  and  to  end  upon  the*  six  surrounding  molecules, 
but  not  to  penetrate  them;  and  if  the  molecules  attract  with 
a  force  varying  inversely  as  the  square  of  the  distance  between 


Do  Molecules  Attract,  Etc.  531 

the  centers  and  directly  as  the  product  of  the  cohesive  masses 
M,  then  the  attraction  of  two  molecules  would  be  M2K/V/3. 
The  pressure  per  square  cm  would  be  M2K/7//3.  Since  the 
attraction  goes  but  a  single  molecular  diameter  we  may 
multiply  the  numerator  and  denominator  by  N4/3,  where  N 
is  the  number  of  molecules  in  the  mass  which  will  make 
N4/3M2K/V4/3.  It  is  obvious  that  this  expression  cannot  be 
true,  for  the  cohesion  varies  inversely  as  the  square  of  the 
volume,  and  not  as  the  4/3d  power.  Assuming,  however, 
that  it  is  correct  we  would  have,  as  the  difference  in  the 
cohesive  energies  in  the  liquid  and  vapor,  the  expres- 
sion: N4/3M2K(i/V/3  -  i/V^/3).  Or  changing  to  density 
N4/3M2K(c/;/3  —  D;/3)/Wt1/3.  Hence  I,  —  E  should  equal  this 
expression,  and  (I,  —  E)/(d'/3  —  D^3)  -  N4/3M2K/Wt1/3  =  /. 
This  last  expression  can  be  tested,  since  M2K  can  be  easily 
computed  from  van  der  Waals  "a"  by  dividing  it  by  N2,  the 
square  of  the  number  of  molecules  in  the  volume  V,  or  Wt; 
and  p.'  is  given  by  Mills.  The  two  values  are  not  of  the  same 
order  of  magnitude.  For  example  in  pentane,  //  is  no, 
whereas  N4/3M2K/Wt1/3  for  i  gram  is  2.214  X  io~13  calories. 
A  constant  very  like  //  is  obtained,  however,  if  the  foregoing 
constant  is  divided  by  V2/3/3N2/3.  This  changes  it  to  the 
expression  3N2M2K/V2/3Wt'/3.  This  would  give  the  value 
1 02  for  pentane.  How  closely  this  constant  agrees  with  Mills 
is  shown  in  Table  i.  N2M2K  is  equal  to  "a." 

The  constant  cannot  be  deduced,  therefore,  by  the 
assumptions  we  have  made,  one  of  them  being  that  molecules 
attract  each  other  inversely  as  the  square  of  the  distance,  but 
it  is  necessary  to  divide  the  theoretical  constant  by 
Vj/3/3N2/3  to  get  that  found.  This  however,  has  the  effect 
of  changing  the  equation,  near  the  critical  temperature,  to 
the  form:  Iy  —  E  =  3a(i/V1  —  i/Vv)  which  is  almost  identical 
with  van  der  Waals. 

This  argument  will  perhaps  be  still  more  convincing  if 
it  be  turned  around.  Let  us  suppose  Mills'  contention  is 
correct  and  the  internal  latent  heat  represents  only  heat  used 
in  overcoming  cohesion,  then  //VJ/8  is  the  cohesive  energy 


532 


Albert  P.  Mathews 


in  the  liquid;  and  ^'/V^8  is  that  in  the  vapor.  If  now  we 
divide  the  first  by  Vl  and  the  second  by  Vw  we  obtain  the 
cohesive  pressure  per  unit  surface  in  the  liquid  and  vapor, 
respectively,  or  ///V]/3  and  /*'/V*/3.  But  we  know  that  the 
cohesive  pressure  is  a/V2,  hence  the  original  assumption  must 
be  incorrect. 

If,  on  the  other  hand,  the  difference  in  the  cohesive 
energy  in  the  liquid  and  vapor  is  equal  to  a(i/V1  -  -  i/Vv), 
and  all  the  latent  heat  is  used  in  overcoming  external  and 
cohesive  pressure,  then  L  —  E  should  equal  this  expression. 
If,  however,  some  of  the  heat,  I,  is  used  in  expanding  the 
molecules  then  the  equation  should  be :  L  —  E  —  I  =  a(i/Vl  - 
i/VJ.  Near  the  critical  temperature  I  becomes  very  small 
and  hence  (L —  E)/(^  -  -  DJ,  near  the  critical  temperature, 
must  be  very  nearly  equal  to  a/Wt,  where  Wt  is  the  weight 
taken  in  grams;  but  at  temperatures  below  the  critical, 
(If  -  -  E)/(^  -  -  DJ  should  be  progressively  greater  than 
a/Wt  by  the  amount  l/(dl  -  -  DJ.  Table  4  shows  that  this 
expectation  is  realized,  since  in  all  cases  the  value  (L  --  E)/- 
(</!  -  -  Dv)  is  greater  below  the  critical  temperature,  but  be- 
comes very  nearly  equal  to  a/Wt  at  the  critical  temperature. 
The  value  "a"  used  in  these  calculations  was  calculated  from 
the  surface  tension  in  the  manner  described.1  j  * 

The  values  diverge  as  the  temperature'falls. 

TABLE  4 — ERGS  FOR  GRAM  MOLECULAR  QUANTITIES 
Diisobutyl  Methyl  acetate 


Temp. 

L  —  E 

N2M2 
K/Wt 

Temp. 

L  —  E 

N2M2 
K/Wt 

d—  D 

d—  D 

— 

— 

100° 

3.025  X  lo11 

100° 

4-768JX  lo11 

200 

2-597 

200 

4-238 

220 

2.414 

260 

3-942 

230 

2.243 

274 

3.660 

233 

2.124 

276.8 

Critical 

3.222 

233-7 

Critical 

2.l6o 

1  Mathews:  Jour,  Phys.  Chem.,  17,  154  (1913). 


Do  Molecules  Attract,  Etc. 


533 


4  —  (Continued) 


Diisopropyl 


Ethyl  acetate 


Temp. 

L  —  E 

N2M2 
K/Wt 

Temp. 

L—  E 

N2M2 
.  K/Wt 

d  —  D 

d  —  D 

100° 

3.808  X  ion 

100° 

3.462 

200 

3.291 

2OO 

3.016 

22O 

3-039 

220 

2.873 

225 

2.895 

240 

2.645 

227.35 

Critical 

2.877 

247 

2.482 

249 

2.472 

250.1 

Critical 

2-357 

Methyl  propionate 


Methyl  formate 


100° 

3.417  X  ro11 

100° 

2.481  X  ion 

200 

3-030 

200 

2.015 

22O 

2.931 

210 

1.842 

250 

2-598 

213 

1-747 

256 

2.396 

213-5 

i  .710 

257-4 

Critical 

2-353 

214 

Critical 

1.791 

Pentane  normal 


Stannic  chloride 


0° 

4.013  X  ion 

100° 

•  573  X  lo11 

40 

3.807 

200 

•413 

100 

3-558 

240 

•358 

1  80 

3-085 

260 

.322 

J95 

2.769 

280 

.280 

197.1 

2.621 

3i8.7 

Critical 

i  .106 

I97.I5 

2.637 

197.2 

Critical 

2.806 

Ethyl  propionate 


Propyl  acetate 


100° 

3.901  X  lo11 

100° 

3-929 

200 

3.385 

200 

3.507 

270 

2.825 

270 

2.860 

272.8 

Critical 

2.552 

275 

2.721 

276.2 

Critical 

2-575 

Benzene 


Ethyl  formate 


80° 

3.486  X  ion 

100° 

2.968  X  ion 

IOO 

3.4I3 

200 

2.532 

140 

3.272 

230 

2.201 

180 

3.197 

234 

2.087 

200 

3.118 

235.3 

Critical 

2.  121 

22O 

3-052 

280 

2.676 

288.5 

Critical 

2.556 

, 

534 


Albert  P.  Mathews 


4 — (Continued) 
Isopentane  Methyl  butyrate 


Temp. 

L—E 

N2M2 
K/Wt 

Temp. 

L  —  E 

K/Wt 

d—  D 

d—  D 

20° 

3.694  X  ion 

IOO 

3.367 

100° 

3  -776 

1  60 

3.067 

200 

3.429 

185 

2.694 

270 

3-033 

187 

2.616 

280 

2-573 

187.4 

2-559 

281.3 

Critical 

2-559 

187.8 

Critical 

2.726 

Heptane 


Ether 


Methyl  isobutyrate 


0° 

5-045 

100° 

3-675 

IOO 

4-730 

200 

3-256 

1  80 

4-3H 

265 

2.687 

220 

4.II4 

266.5 

2  .620 

260 

3.668 

267.55 

Critical 

2.488 

266 

3-428 

266.5 

3-343 

266.85 

Critical 

3.i87 

Carbon  tetrachloride 


0° 

3.596 

0° 

.907 

20 

3-48I 

80 

.823 

IOO 

3.160 

IOO 

.792 

1  80 

2.708 

120 

.756 

190 

2.516 

1  80 

.661 

193 

2.332 

200 

•590 

193-4 

Critical 

2.468 

260 

•520 

280 

I.4I9 

283.15 

Critical 

1-383 

Hexane                                       Fluorbenzene 

0° 

80 

IOO 

1  80 
200 

234 
234.8 

4.504 
4.217 
4.128 
3.684 
3-568 
3.004 
Critical 

3.003 

80° 

200 
286.55 

3-096 
2.672 

Critical 

2.391 

It  is  of  interest  to  see  how  large  the  amount  of  heat  (I) 
is  which  is  absorbed  intramolecularly  on  passing  from  liquid 
to  vapor.  Table  5  contains  the  calculations  for  I  of  i  gram 
of  hexane.  I  =  I,  —  E  —  a(i/Vj  --  i/Vw)  gram  calories. 


Do  Molecules  Attract,  Etc. 


535 


TABLE  5 — HEXANE 


i 

L  —  E 

I 

0° 

84.68 

28.21  Calories 

60 

73-59 

21.88 

80 

70.04 

20.  17 

IOO 

65-82 

18.06 

1  80 

44-30 

8.19 

200 

37.00 

5-86 

230 

16.98 

o-93 

234 

8.98 

0.00 

234-5 

o.oo 

o.oo  Critical 

The  intramolecular  heat  (I)  absorbed  is  obviously  con- 
siderable.1 At  corresponding  temperatures  the  amount  of 
intramolecular  latent  heat  is  for  gram  mol  quantities,  greater, 
the  larger  the  number  of  atoms  in  the  molecule  as  may  be  seen 
in  Table  4. 

The  conclusion  is,  therefore,  that  van  der  Waals'  re- 
lationship, i.  e.,  I,  --  E  =  a(i/V1  --  i/Vw)  is  correct  close  to 
the  critical  temperature,  but  should  be  changed  to  the  form 
I,  -  -  E  -  -  I  =  a(i/V1  -  -  i/Vw),  where  I  is  the  heat  made 
latent  intramolecularly  by  expansion  of  the  molecules,  or 
increasing  rotation,  in  passing  from  the  liquid  to  the  vapor; 
and  that  while  Mills  relationship:  L  -  -  E  =  //(i/V1/3  - 
i/V^/3)  is  empirically  true  except,  possibly,  near  the  critical 
temperature,  yet  since  L  -  -  E  does  not  represent  solely  the 
increase  in  potential  energy  due  to  the  separation  of  the  mole- 
cules, the  inference  he  has  drawn  from  it,  that  molecules 
attract  inversely  as  the  square  of  the  distance,  is  not  justified. 
On  the  other  hand,  the  correct  expression  for  the  increase  of 
molecular  potential  energy,  a/(i/V,  —  i/VJ,  is  obtained  very 
simply  if  the  molecules  attract  inversely  as  the  fourth  power 
of  the  distance,  as  Sutherland  has  shown. 

University  of  Chicago 


1  "a  "  should  be  larger  and  the  figures  in  column  3  should  be  somewhat 
smaller.     See  footnote  p.  525. 


THE    SIGNIFICANCE    OF    THE    RELATIONSHIP    BE- 
TWEEN MOLECULAR  COHESION  AND  THE  PROD- 
UCT OF  THE  MOLECULAR  WEIGHT  AND  THE 
NUMBER  OF  VALENCES 


BY  ALBERT  p.  MATHEWS 

In  the  preceding  papers1  of  this  series  I  have  shown  that 
the  value  of  "a"  of  van  der  Waals,  representing  molecular 
cohesion,  or  the  value  M2K  which  is  the  factor  "a"  for  a 
single  molecule,  is  proportional  to  the  two-thirds  power  of  the 
product  of  the  molecular  weight  by  the  number  of  valences 
of  the  molecule.  M2K  was  found  to  be  equal,  when  expressed 
in  absolute  units,  to  2.98  X  io~37  (Mol.  Wt.  X  No.  of  Val.)2/3. 

In  this  paper  I  shall  discuss  the  theoretical  bearing  of  the 
relationship  of  cohesion  to  these  molecular  properties. 

Attempts  have  been  made  by  others  to  correlate  cohesion, 
or  "a,"  with  molecular  weight  and  the  number  of  valences, 
but  with  very  partial  success.  Sutherland2  at  first  supposed 
the  molecular  attraction  to  be  proportional  to  the  product 
of  the  gravitational  masses  of  the  molecules.  This  he  found 
would  not  do,  and  in  his  later  papers  he  stated  that  the  gravita- 
tional mass  of  a  molecule  did  not  enter  into  the  expression 
"a."  Amagat,3  also,  recently  revived  the  idea  that  gravita- 
tional mass  plays  a  role  in  cohesion  and  suggested  that  a/V2 
ought  to  be  proportional  to  the  square  of  the  molecular  mass. 
This,  however,  he  did  not  find  to  be  the  case.  Leduc4  has 
recently  confirmed,  in  part,  this  view  of  Amagat 's  for  gases  of 
similar  molecular  composition,  when  taken  under  the  same 
volume  and  at  corresponding  temperatures.  Kleeman,5  also 
has  tried  to  find  a  relationship  between  "a"  and  gravita- 


1  Mathews:  Jour.  Phys.  Chem.,  17,  154  (1913)- 

2  Sutherland:  Phil.  Mag.,  [5]  27,  305  (1889);   [6]  4,  632  (1902). 

3  Amagat:  "Pression  interne  des  fluides,"  Journal  de  Physique,    [4]   8, 
617  (1909). 

*  Leduc:  Comptes  rendus,  153,  179  (1911). 

8  Kleeman:  Phil.  Mag.,  [6]  19,  783,  840-847  {1910). 


482  Albert  P.  Mathews 

tional  mass,  and  states  that  the  cohesive  attraction  of  two 
molecules  is  proportional  to  the  product  of  the  two  sums  of 
the  square  roots  of  the  atomic  weights  of  the  atoms  of  the 
molecules.  This  relationship,  however,  is  of  very  limited 
applicability,  if  indeed,  it  correctly  expresses  the  cohesion  of 
any. 

As  regards  valence,  I  can  find  but  one  other  suggestion, 
that  of  Sutherland.1  He  showed  that  the  number  of  equiva- 
lents, or  valences,  in  simple  substances,  such  as  sodium 
chloride,  influenced  the  value  of  their  cohesion.  He  was 
unable  to 'establish  this  relationship  for  more  complex  bodies. 
Nevertheless  he  assumed  that  it  existed  in  them  and  correctly 
surmised  from  it  the  relationship  between  cohesion  and 
chemical  affinity,  and  adduced  it  as  evidence  of  the  electro- 
static or  magnetic  nature  of  cohesion,  "a"  was  made  pro- 
portional to  the  square  root  of  the  valence. 

The  relationship  between  cohesion  and  the  properties  of 
molecular  weight  and  the  number  of  valences  can  be  inter- 
preted best  by  Sir  J.  J.  Thomson's  theory  of  the  electrical 
constitution  of  matter  and  valence,  and,  so  far  as  I  can  see, 
on  no  other  hypothesis.  It  speaks,  therefore,  for  the  electro- 
static, or  electro-magnetic  theory  of  cohesion,  and,  in  my 
opinion,  for  the  latter. 

The  relation,  M2K  =  (/)(Val">VMol.  WtJ/s,  seems  at  first 
peculiar.  It  is  odd  that  the  valence  of  an  atom  should  be  of 
as  much  importance  in  cohesion  as  the  weight  of  the  atom; 
it  is  a  relationship  which  one  would  not  have  anticipated. 
The  significance  of  this  fact,  if  I  am  not  mistaken,  is  that  the 
electron  couples  constituting  the  molecules  are  of  two  kinds, 
namely,  those  of  the  atoms  themselves,  which  added  together 
presumably  give  the  molecular  weight;  and  the  valence  elec- 
trons, which  differ  from  the  others  so  that  they  cannot  be 
added  to  them.  Hence  the  formula  is  not  M2K  =  (/)  (Wt.  + 
Val.),  the  cohesion  being  proportional  to  the  sum;  but  the 
mass  of  cohesion  is  proportional  to  the  cube  root  of  each  of 

1  Sutherland:  Phil.  Mag.,  [6]  4,  632  (1902). 


Relationship  between  Molecular  Cohesion  483 

these  kinds  of  electrons  and  so  is  proportional  to  the  cube  root 
of  their  product.  The  valence  electrons  are  probably  more 
labile,  more  easily  removed  and  replaced.  They  have  a 
different  degree  of  liberty  and  they  cannot  be  summed  with 
the  atomic. 

The  formula  thus  confirms  the  correctness  of  Drude's 
promise  that  the  electrons  of  the  valences  differ  in  their 
properties  from  the  electrons  of  the  atoms.  He  concluded 
that  only  the  valence  electrons  would  be  sufficiently  free  to 
vibrate  synchronously  with  light  and  hence  these  electrons 
must  be  particularly  concerned  in  the  refraction  and  dis- 
persion of  light.  Drude's1  suggestion  of  electrons  of  different 
degrees  of  liberty  confirmed,  as  it  was,  by  experiments  show- 
ing a  relation  between  valence  and  dispersion,  is  thus  con- 
firmed also  from  the  wholly  different  field  of  cohesion. 

A  still  more  interesting  conclusion  may  be  drawn  from 
this  relationship,  namely,  that  a  neutral,  uncharged  atom 
having  no  valence  will  have  no  cohesion.  Since  it  will  have 
no  chemical  affinity  either,  if  chemical  affinity  is,  as  it  ap- 
pears to  be,  of  an  electrical  nature,  it  is  thus  seen  that  a  close 
relation  must  exist  between  chemical  affinity  and  cohesion. 
Such  neutral  atoms  will  presumably  still  have  gravitational 
attraction.  A  free  electrical  charge  on  the  atom  is,  therefore, 
necessary  for  cohesion,  but  not  for  gravitation.  Furthermore, 
the  cohesional  effect  is  the  same  whether  the  charge  be  positive 
or  negative;  and  it  is  proportional  to  the  number  of  charges. 
The  formula  shows,  also,  that  the  effect  of  a  free  charge  on  any 
atom  is  proportional  to  the  weight  of  the  atom;  that  is,  the 
effect  of  the  valence  charge  is  multiplied,  as  it  were,  by  the 
number  of  electron  couples  in  the  atom;  and  the  effect  of  the 
total  number  of  valence  charges  in  the  molecule  is  multiplied 
by  the  whole  number  of  atomic  electron  couples  in  the  mole- 
cule. Just  how  such  an  effect  could  be  produced,  and  why  the 
attraction,  or  cohesive  mass,  should  ultimately  prove  to  be 
proportional  to  a  linear  function  (the  cube  root)  of  the  product 


Drude:  Annalen  der  Physik.,  [4]  14,  677  (1904)- 


484  Albert  P.  Mathews 

of  the  number  of  valences  by  the  molecular  weight,  I  do  not 
see. 

It  appears,  then,  that  refraction,  dispersion  and  cohesion 
all  involve  the  valence  electrons,  but  the  connection  between 
cohesion  and  valence  is  far  closer  and  simpler  than  the  other 
relationships  appear  to  be.  The  relationship  of  valence  to 
light  is  necessarily  a  less  direct  one,  refraction  depending 
on  the  rate  of  vibration  of  the  electron.  It  is  said1  that  if  the 
natural  period  of  the  molecule  (electron)  is  slightly  less  than 
the  frequency  of  a  light  wave  the  light  will  be  accelerated; 
if  greater,  retarded.  It  is  evident  that  in  dispersion  other 
properties  of  the  electrons  than  number  come  into  play,  and, 
hence,  the  relationship  between  dispersion  and  number  is 
not  so  simple  and  direct.  Double  bonds,  neighboring  groups, 
etc.,  influence  the  periods  of  the  electrons  and  so  influence  the 
dispersive  power;  whereas  these  factors  appear  to  play  no 
important  part  in  cohesion. 

The  relation  between  the  refraction  of  light  of  one  wave 
length  and  the  valence  number  is  still  less  direct  than  be- 
tween dispersion  and  valence,  but  still  a  general  relation 
exists  which  for  substances  of  the  same  type  is  rather  uniform, 
as  shown  by  Traube2  for  many  liquids  and  by  Cuthbertson3 
for  several  gases. 

Another  very  interesting  fact  correlating  the  refractive  and 
cohesive  properties  of  matter  is  the  resemblance  between  the 
constant  "K"  of  the  Ketteler  dispersion  formula  and  the 
value  M2K  of  cohesion.  Thus  with  the  Ketteler  formula 
n2  =  a2  —  K  P  +  D  X\/(P  —  Pv)  the  constant  "K,"  Drude 
found,  could  be  computed  with  a  fair  approximation,  in  some 
cases  at  any  rate,  from  the  sum  of  the  valences,  the  molecular 
weight  and  the  density,  and  this  result  was  confirmed  by 
Erfle.4  This  constant  "K,"  therefore,  contains  at  least 


1  Cotter,  J.  R.:  "Dispersion,"  Encyclo.  Brit.,  nth  edition,  8,  317. 

2  Traube:  Ber.  chem.  Ges.  Berlin,  40,  130  (1907). 

3  Cuthbertson:  Proc.  Roy.  Soc.,  8aA  (1909-1910);  Phil.  Mag.,   [6]  21,  69 
(1911);  Phil.  Trans.,  204,  323  (1905);  207,  135  (1907). 

4  Erne:  "Optische  Eigenschaften  und  Elektronen  Theorie."     Annalen  der 
Physik,  [4]  24  (1907). 


Relationship  between  Molecular  Cohesion  485 

sometimes  the  same  factors  as  the  value  a/V2  of  van^der 
Waals'  equation.  I  have  not,  however,  attempted  to  estab- 
lish any  closer  connection  between  them.1 

We  conclude,  therefore,  that  while  cohesion  and  re- 
fractivity  are  both  dependent  on  a  common  factor,  namely 
the  valence  electrons,  and  possibly  upon  the  molecular  weight, 
the  connection  between  them  is  not  direct,  but  indirect; 
and  while  cohesion  and  refraction,  or  dispersion,  often  parallel 
each  other,  they,  at  other  times,  diverge  considerably  since 
other  factors  enter  into  refraction. 

It  is  not  without  interest  to  recall  as  an  example  of  the 
perspicacity  of  genius,  that  I^aplace2  long  ago  foretold  a  con- 
nection between  these  properties.  Writing  in  1805  of  the 
formula  of  capillarity  which,  as  will  be  remembered,  con- 
tained two  terms,  -one  K,  representing  molecular  cohesion, 
or  van  der  Waals'  expression  a/V;  the  other,  H,  the  capillary 
constant,  Laplace  says  (p.  351):  "I  saw  that  this  action 
(pressure)  is  smaller  or  larger  than  if  the  surface  is  plane; 
smaller,  if  the  surface  is  concave;  larger,  if  it  is  convex.  Its 
analytical  expression  is  composed  of  two  terms:  the  first 
(K),  much  larger  than  the  second,  expresses  the  action  of  the 
mass  terminated  by  a  plane  surface;  and  I  think  from  this 
term  depends  the  suspension  of  mercury  in  a  barometer  tube 
at  a  height  two  to  three  times  greater  than  that  due  to 
atmospheric  pressure,  the  refractive  powers  of  diaphanous 
bodies,  the  cohesion,  and  in  general,  chemical  affinity;  the 
second  term  expresses  the  part  of  the  action  due  to  the  spheri- 
city of  the  surface."  And  again  (p.  362):  "The  function,  K, 
is  analogous  to  that  I  have  designated  by  the  same  letter  in 
the  refraction  of  light." 

But  of  even  greater  interest  and  more  fundamental 
importance  than  the  relation  between  the  optical  and  the 
cohesive  properties,  which  is  now  understandable  since  both 


1  See  also  Natanson:  Bull,  de  1'Acad.  des  Sci.  de  Cracovie,  1907,  April 
p.  316  for  the  relation  of  refraction  and  valence. 

2  Laplace:   Sur   1'action   capillaire.    Oeuvres.    Supp.    Liv.   X,   Trait£   de 
Mecanique  Celeste,  p.  351. 


486  Albert  P.  Mathews 

involve  the  number  of  valence  electrons,  is  the  relation  be- 
tween the  magnetic  and  cohesive  properties,  since  here  we 
touch,  I  think,  the  very  kernel  of  the  problem  of  the  nature 
of  cohesion. 

The  connection  between  the  magnetic  properties  and 
cohesion  is  brought  out  very  clearly,  in  an  empirical  way, 
by  Pascal's1  investigations  on  the  relation  between  magnetic 
susceptibility  and  the  molecular  properties.  In  a  series  of 
papers  Pascal  has  shown  that  there  is  a  remarkable  con- 
nection between  the  specific  susceptibility  of  diamagnetic 
elements  and  the  atomic  weights  and  valences.  Thus  if 
elements  of  the  same  family  having  the  same  valence  are 
arranged  in  their  order  of  increasing  specific  susceptibility, 
they  are  in  the  order  of  their  atomic  weights;  and,  on  the 
other  hand,  a  close  dependence  on  valence  may  be  observed. 
In  elements  of  nearly  the  same  weight  but  of  different  valence 
numbers,  the  atomic  magnetic  susceptibility,  XH,  increases 
with  the  number  of  valences.  An  empirical  relationship 
was  found  between  them,  Xa  —  io~7ett  +  fta  where  a  is 

about  2.1,  ft  about  0.004  and  a  the  atomic  weight,  a  and  ft 
depend  only  on  valence.  But  here,  also,  double  bonds  made 
their  effect  felt,  though  less  pronouncedly  than  in  refraction. 
Double  bonded  molecules  have,  in  general,  a  lower  molecular 
susceptibility  than  that  calculated.  Other  effects  of  molecular 
form  are  seen;  for  example,  the  benzene  nucleus  augments 
the  diamagnetism,  although  the  double  bonds  it  is  supposed 
to  contain  should  have  an  opposite  effect.  The  factor  of 
molecular  structure  appears,  then,  to  influence  diamagnetism. 
On  the  whole,  however,  calculation  of  the  number  of  valences 
in  the  molecule  by  this  procedure  agrees  better  with  the  calcu- 
lation from  the  cohesion,  than  does  the  calculation  from  the 
refractivity  or  dispersion.  Thus,  double  bonds  are  of  less 
action  on  the  diamagnetism  and  in  the  benzene  nucleus  they 


1  Pascal :  '  'Sur  un  mode  de  contr61e  optique  des  analyses  magpie"  tochimiques," 
Comptes  rendus,  152,  1852  (1911).  Recherches  magneto-chimiques  sur  la  struc- 
ture atomique  des  halogenes,"  Comptes  rendus,  152,  826  (1911).  Ann.  Chim. 
Phys.,  [8]  19,  1-80  (1910). 


Relationship  between  Molecular  Cohesion  487 

appear  to  exert  no  effect.  By  this  method,  as  by  the  cohesional, 
all  organic  chlorine  compounds  examined  were  found  to  have 
trivalent  chlorine  and  fluorine  was  monovalent.  The  agree- 
ment was  good  in  regard  to  other  elements  also. 

The  connection  between  cohesion  and  diamagnetism  is, 
therefore,  again  an  indirect  one.  Both  involve  the  molecular 
weight  and  the  number  of  valences,  but  it  is  clear  that  cohesion 
is  independent  of  molecular  form,  or  very  largely  so;  whereas 
whether  a  substance  is  magnetic,  or  diamagnetic,  may  depend, 
in  part  upon  this  very  factor.  Oxygen  in  an  elemental  form, 
is  paramagnetic,  not  diamagnetic,  and  is  quite  anomalous  in 
Pascal's  scheme;  whereas  the  cohesion  of  oxygen  is  not  anomal- 
ous. In  other  words,  whether  a  body  is,  as  a  whole,  para- 
magnetic or  diamagnetic,  and  to  what  degree,  depends,  prob- 
ably, on  the  possibility  of  the  orientation  of  the  molecules, 
their  polarity,  etc.,  factors  which  do  not  seem  to  affect  their 
cohesion  or  gravitation.  Nevertheless  cohesion  and  magnetic 
properties  are,  no  doubt,  closely  related,  since  both  depend 
on  the  same  molecular  properties,  only  magnetism  involves 
still  other  properties,  (form)  not  involved  in  cohesion. 

The  fact  that  cohesion  is  thus  determined  by  the  number 
of  electron  couples  (atomic  and  valence)  in  the  molecule 
plainly  points  toward  the  conclusion  that  cohesion  is  either 
electro-static  or  electro-magnetic  in  nature.  Both  of  these 
possibilities  have  already  been  suggested.  Sutherland,  *  from 
his  discovery  of  the  relation  of  cohesion  to  valence  in  salts, 
inferred  at  first  that  the  cohesion  must  be  of  an  electromagnetic 
nature.  He  supposed  these  rotating  electron  couples  acted 
like  little  magnets,  and  he  attempted  to  show,  though  whether 
successfully,  or  not,  I  am  unable  to  judge,  that  small  magnets, 
at  sufficient  distances  apart,  would  attract  inversely  as  the 
fourth  power  of  the  distance  between  them,  and  this  he  sup- 
posed to  be  the  law  of  molecular  attraction.  This  conclusion 
was  attacked  by  van  der  Waals,  Jr.,2  who  concluded,  also 

1  Sutherland:  Phil.  Mag.,  [6]  19,  i  (1910);  4,  625  (1902). 

2  Van  der  Waals,  Jr. :  Kon.   Akad.   v.   Wetensch.   te  Amsterdam,   Pro- 
ceedings, n,  132  (1908-1909). 


488  Albert  P.  Mathews 

from  mathematical  reasoning,  that  the  attraction  between 
such  magnets  would  be  inversely  as  the  yth  or  9th  power  of 
the  distance,  and  thus  agree  with  the  assumptions  of  his  father, 
that  molecular  attraction  diminished  at  such  a  rate  that  it 
was  effective  only  when  the  molecules  were  in  contact.  Later, 
Sutherland1  concluded  that  cohesional  attraction  was  due  to 
electrostatic  affinity  of  these  electron  couples.  Lodge2  made 
a  similar  suggestion.  He  thought  some  of  the  lines  of  force 
between  the  atoms  wandered  outside  the  molecule  to  atoms  of 
other  molecules  and  thus  produced  molecular  cohesion.  This 
would  make  molecular  cohesion  of  the  same  nature  as  chemical 
affinity.  While  the  relation  between  the  two  is  close,  both 
being  zero  in  the  absence  of  an  electric  charge,  or  valence, 
one  is  not  causally  dependent  on  the  other,  although  both 
depend  on  the  valences.  The  attraction  between  the  atoms 
is  probably  of  an  electrostatic  kind  and,  if  so,  should  vary 
inversely  as  the  square  of  the  distance.  The  atomic  weight 
does  not  appear  to  play  a  part  in  chemical  affinity,  for  very 
light  elements  may  enter  into  very  firm  union.  In  cohesion, 
molecular  weight  does  play  a  large  part;  and  while  it  is  not 
impossible  that  the  cohesional  attraction  may  be  inversely 
as  the  square  of  the  distance,  it  is  not  probable,  or  at  any 
rate  it  has  not  yet  been  proved  to  general  satisfaction. 

It  seems  much  more  probable  to  me  that  cohesion  is  more 
closely  related  to  magnetism  than  to  electrostatic  affinity 
and  I  would  raise  the  question  whether  magnetism  is  anything 
else  than  molecular  cohesion  made  apparent  at  distances 
more  than  molecular.  Is  it  not  possible  that  molecular  cohe- 
sion, involving  as  it  does  both  atomic  and  valence  electrons 
(atomic  weight  and  valence)  is  due,  perhaps,  to  the  magnetic 
effects  produced  by  the  movements  of  these  electron  couples? 
In  this  view  the  atoms  would  be  united  by  their  electro- 
static affinities  and  these  same  valences  and  the  other  atomic 
electrons  by  their  magnetic  effects  produce  the  molecular 


1  Sutherland:  Phil.  Mag.,  [6]  17,  667  (1909). 

2  Lodge:  Nature,  70,  176  (1904). 


Relationship  between  Molecular  Cohesion  489 

cohesion.  I  may  state  briefly  some  of  the  reasons  which  ap- 
pear to  lead  to  such  a  conclusion. 

In  the  first  place  we  have  the  surprising  fact  that  the 
field  of  cohesion  of  a  molecule  is  apparently  delimited  by 
the  surrounding  molecules.  The  evidence  for  this,  while 
perhaps  not  conclusive,  is  both  direct  and  indirect.  The 
reason  for  the  shortness  of  the  radius  of  action  of  cohesion  is 
one  of  the  most  interesting  questions  of  molecular  physics. 
It  is  of  interest  to  see  how  this  question  came  to  be  generally 
considered  closed  and  settled  in  favor  of  the  view,  now  gener- 
ally accepted,  that  cohesional  attraction  diminishes  with  the 
distance  at  a  rate  far  greater  than  gravitational  attraction. 
It  is  chiefly  due  to  Laplace. 

Laplace,1  in  his  beautiful  memoir  on  capillarity,  first 
raised  the  question  whether  the  short  radius  of  attraction 
of  the  cohesive  forces  was  due  to  the  fact  that  matter  shut 
off  the  attraction,  or  was  due  to  the  attraction  diminishing 
with  the  distance  at  a  rate  far  more  rapid  than  gravitation. 

He  says,  when  discussing  Hawksbee's  well-known  ex- 
periments proving  that  the  height  to  which  water  rises  in  a 
glass  tube  is  independent  of  the  thickness  of  the  wall  of  the 
tube:  "Hawksbee  a  observe  que  dans  les  tubes  de  verre, 
ou  tres  minces  ou  tres  epais,  1'eau  s'elevait  a  la  meme  hauteur 
toutes  les  fois  que  les  diametres  interieurs  etaient  les  memes. 
Les  couches  cylindriques  du  verre  qui  sont  a  une  distance 
sensible  de  la  surface  interieure  ne  contribuent  done  point  a 
1' ascension  de  1'eau,  quoique  dans  chacune  d'elles,  prise 
separement,  ce  fluide  doive  s'elever  au-dessus  du  niveau. 
Ce  n'est  point  1'interposition  des  couches  qu'elles  embrassent 
qui  arrete  leur  action  sur  1'eau,  car  il  est  naturel  de  penser 
que  les  attractions  capillaires  se  transmettent  a  travers  les  corps, 
ainsi  que  la  pesanteur;  cette  action  ne  disparait  done  qu'a  raison 
de  la  distance  du  fluide  a  ces  couches,  d'ou  il  suit  que  V 'attraction 
du  verre  sur  Veau  n'est  sensible  qu'a  des  distances  insensibles." 
I  have  italicized  the  end  of  Laplace's  statement  to  bring  out 

1  Laplace:  "Sur  1'action  capillaire.  Oeuvres.  Supp.  au  Livre  X,"  Traite  de 
Mecanique  Celeste,  p.  351;  see  also  p.  487. 


490  Albert  P.  Mathews 

clearly  the  reason  which  led  him  to  the  conclusion  that  molecu- 
lar cohesion  penetrated  matter  like  gravitation,  and  that  the 
attraction  must,  hence,  decrease  very  rapidly  with  the  dis- 
tance. It  will  be  seen  that  the  sole  reason  for  his  decision 
was  the  possible  analogy  between  gravitation  and  molecular 
cohesion. 

The  very  important  result  of  the  rejection  by  Laplace 
of  the  possibility  of  cohesive  attraction  not  penetrating  matter 
was  that  it  forced  him  to  the  conclusion  that  the  cohesive 
force  must  diminish  far  more  rapidly  than  gravitation  as  the 
distance  increases.  Laplace  did  not  make  any  assumption 
as  to  the  rate  at  which  the  cohesional  attraction  diminished 
with  the  distance,  except  that  it  was  at  so  rapid  a  rate  that 
the  cohesion  became  negligible  within  all  measurable  dis- 
tances. 

The  great  English  philosopher,  Thomas  Young,1  who 
a  year  before  Laplace  had  shown  the  true  nature  of  surface 
tension  and  practically  anticipated  all  of  Laplace's  main 
conclusions,  does  not  appear  to  have  raised  the  question  in 
a  concrete  form.  His  papers  on  capillarity  are  so  condensed 
that  the  reasoning  is  very  difficult  to  follow.2 

But  while  Young  nowhere  specifically  puts  the  question 
whether  the  cohesional  attraction  penetrates  matter,  he 
made  an  assumption  which  might  be  taken  to  indicate  that 
it  does  not.  "We  may  suppose,"  he  says  (p.  43),  "the  parti- 
cles of  liquids,  and  probably  those  of  solids  also,  to  possess 
that  power  of  repulsion  which  has  been  demonstratively 
shown  by  Newton  to  exist  in  aeriform  fluids,  and  which  varies 
as  the  simple  inverse  ratio  of  the  distance  of  the  particles 
from  each  other.  In  air  and  vapors  this  force  appears  to  act 


1  Young:  "An   Essay   on   the   Cohesion   of   Fluids,"    Phil.   Trans.,    1805 
(collected  works,  edited  by  G.  Peacock,  i,  418  (1855),  London). 

2  A  propos  of  this  paper  of  Young's,  Clerk  Maxwell  makes  an  interesting 
comment.     He  says:  "His    [Young's]  essay  contains  the  solution  of  a  great 
number  of  cases  including  most  of  those  afterwards  solved  by  Laplace;  but  his 
methods  of  demonstration,  though  always  correct  and  often  extremely  elegant, 
are  sometimes  rendered  obscure  by  his  scrupulous  avoidance  of  mathematical 
symbols."     Ency.  Brit.,  Article,  "Capillarity." 


Relationship  between  Molecular  Cohesion  491 

uncontrolled;  but  in  liquids  it  is  overcome  by  a  cohesive  force, 
while  the  particles  still  retain  a  power  of  moving  freely  in  all 
directions;  and  in  solids  the  same  cohesion  is  accompanied 
by  a  stronger  or  weaker  resistance  to  all  lateral  motion,  which 
is  perfectly  independent  of  the  cohesive  force  and  which  must 
be  cautiously  distinguished  from  it."  "//  is  sufficient  to 
suppose  the  force  of  cohesion  nearly  or  perfectly  constant  in  its 
magnitude  throughout  the  minute  distance  to  which  it  extends, 
and  owing  its  apparent  diversity  to  the  contrary  action  of 
the  repulsive  force,  which  varies  with  the  distance.  Now, 
in  the  internal  parts  of  a  liquid,  these  forces  hold  each  other 
in  a  perfect  equilibrium,  the  particles  being  brought  so  near 
that  the  repulsion  becomes  precisely  equal  to  the  cohesive 
force  that  urges  them  together,"  etc. 

Young  thus  assumed  that  the  cohesion  extended  but 
a  short  distance,  with  slight  variation  in  intensity  and  that 
it  then  ended  abruptly.  So  far  as  I  can  find,  he  made  no 
suggestion  how  it  came  to  end  abruptly;  but  if  it  be  assumed 
that  it  does  not  penetrate  matter,  it  is  seen  that  it  must  end 
abruptly  at  the  next  layer  of  molecules.  Young  tried  to  esti- 
mate how  far  the  cohesive  force  really  extended,  and  found  a 
value  surprisingly  near  the  order  of  magnitude  of  that  now 
known  to  be  the  distance  apart  of  the  centers  of  two  molecules. 
His  reasoning  on  this  point  is  extremely  ingenious,  and  is 
of  interest  as  the  first  estimate  of  molecular  dimensions. 

lyord  Rayleigh1  says  anent  this  computation  of  Young's: 
"One  of  the  most  remarkable  features  of  Young's  treatise  is 
his  estimate  of  the  range  "a"  of  the  attractive  force  on  the 
basis  of  the  relation  T  =  V3aK.  Never  once  have  I  seen  it 
alluded  to,  and  it  is,  I  believe,  generally  supposed  that  the 
first  attempt  of  this  kind  is  not  more  than  twenty  years  old. 
It  detracts  nothing  from  the  merit  of  this  wonderful  specu- 
lation that  a  more  precise  calculation  does  not  verify  the 
numerical  coefficient  in  Young's  equation.  The  point  is 

1  Rayleigh:  "On  the  Theory  of  Surface  Forces,"  Phil.  Mag.,  [5]  30,  285-298, 
456-475  (1890).     Collected  papers,  3,  396. 


492  Albert  P.  Mathews 

that  the  range  of  the  cohesive  forces  is  necessarily  of  the 
order  T/K."  T  is  the  surface  tension  and  K  the  internal 
pressure.  Lord  Rayleigh,  in  his  revision  of  Maxwell's  classical 
account  of  capillarity  in  the  new  edition  of  the  Encyclopaedia 
Britannica  and  in  his  many  splendid  writings  on  this  subject, 
does  not  seem  to  have  considered  this  question.  All  other 
writers  whom  I  have  consulted  seem  to  have  followed  Laplace's 
lead  and  assumed,  without  evidence,  that  cohesion  does 
penetrate  matter  like  gravitation. 

Thus,  Gauss,1  who  introduced  clear  ideas  of  surface 
energy  and  the  potential  energy  of  fluids,  writes  as  follows 
in  1830:  "The  ordinary  attraction  which  is  proportional 
to  the  square  of  the  distance,  and  which  permits  the  repre- 
sentation of  all  motions  in  the  heavens  with  such  good  agree- 
ment, can  be  used  in  the  explanation  neither  of  capillary 
phenomena  nor  of  adhesion  and  cohesion;  a  correctly  carried 
out  computation  shows  '  dass  eine  nach  diesem  Gesetze  wirk- 
ende  Anziehung  eines  beliebigen  Korpers  der  zur  Ausfuhrung 
von  Experimenten  geeignet  ist,  d.  h.,  dessen  Masse  im  Ver- 
gleich  mit  der  der  Erde  vernachlassigt  werden  kann,  auf 
einem  beliebig  gelegenen,  sogar  den  Korper  beriihrenden 
Punkt,  im  Vergleich  mit  der  Schwere  verschwinden  muss. 
Wir  schliessen  hieraus  dass  jenes  Anziehungsgesetz  in  den 
kleinsten  Abstanden  mit  der  Wahrheit  nicht  mehr  iiberein- 
stimmt,  sondern  dass  es  eine  Modification  erfordert. '  In 
other  words,  the  particles  of  the  body  exert,  besides  the  at- 
tractive force  of  gravitations,  still  another  force  which  is  notice- 
able only ,  in  the  smallest  distances.  All  appearances  show 
uniformly  that  the  second  part  of  the  attractive  force  (the 
molecular  attraction)  is  not  noticeable  in  the  smallest  meas- 
urable distances.  On  the  other  hand,  in  unmeasurably  small 
distances  it  may  greatly  surpass  the  first,  which  is  propor- 
tioned to  the  square  of  the  distance. 


1  Gauss:  "Allgemeine  Grundlagen  einer  Theorie  der  Gestalt  von  Fliis- 
sigkeiten,"  Ostwald's  "Klassiker  der  exakten  Wissenschaften,"  No.  135,  p.  i. 
"Commentationes  societatis  Regiae  Scientiarium  Gottingensis  Recentiores,"  vii, 
1830. 


Relationship  between  Molecular  Cohesion  493 

It  was  necessary  for  him  (p.  21),  to  make  some  assump- 
tions regarding  the  cohesional  attraction  which  he  represented 
as  "/"  (r)>  r  being  the  radius  of  molecular  action,  and  he 
accordingly  adopted  Laplace's  view  that  /  (r)  decreases  far 
more  rapidly  than  i/r2,  which  is  the  law  of  gravitational 
attraction  (p.  22).  He  says,  speaking  of  cohesional  attrac- 
tion, or  /  (r) :  "Da  dieser  Ausdruck  etwas  unbestimmtes 
hat  so  lange  wir  nicht  eine  Einheit  zu  Grunde  legen,  wollen 
wir  vor  allem  darauf  aufmerksam  machen,  dass  wir  die  anzie- 
hende  Kraft  /  (r),  ausgedriickt  als  eine  Function  des  Abstandes 
r,  mit  einer  Masse  multipliziert  denken  mussen,  damit  sie 
mit  der  Gravitation  g  in  den  Dimensionen  ubereinstimmt. 
Der  Sinn  unserer  Voraussetzung  ist  dann  der  folgende :  Bezeich- 
net  M  irgend  eine  Masse  derart,  wie  sie  uns  in  Experimenten 
vorkommt,  namlich  eine,  die  im  Vergleich  mit  der  ganzen 
Erde  als  verschwindend  angesehen  werden  kann,  dann  muss 
M  /  (r)  immer  merklich  sein  im  Vergleich  mit  der  Schwere, 
so  lange  r  einen  unseren  Messungen  zuganglichen,  wenn  auch 
noch  so  kleinen  Wert  hat." 

Van  der  Waals,  in  all  his  earlier  writings,  including  his 
famous  essay  on  the  continuity  of  the  gaseous  and  liquid 
states  published  in  1869,  assumed  with  Laplace  that  molec- 
ular cohesion  was  appreciable  only  very  close  to  the  molecule ; 
indeed,  the  radius  of  action  was  less  than  the  mean  distance 
apart  of  the  molecular  centers.  I  have  not  been  able  to  find 
in  his  essays  any  specific  discussion  of  the  question  whether 
cohesional  attraction  penetrates  matter,  although  he  does 
discuss  the  radius  of  attraction  of  a  molecule.1  His  general 
assumption  was  that  the  cohesion  diminished  very  rapidly 
as  the  molecules  separated.  In  one  brief  communication  to 
the  Amsterdam  Academy  of  Sciences  (1893-94,  pp.  20-21)  he 
states  that  he  had  derived  a  potential  function,  that  is,  a 
function  expressing  the  potential  energy  of  attraction  of  two 


1  Van  der  Waals:  "Bijdrage  tot  de  Kennis  van  de  Wet  der  Overeenstem- 
mende  Toestanden,"  Verhandelingen  Konik.  Akad.  van  Wettenschappen,  21,  5 
(1881). 


494  Albert  P.  Mathews 


molecules,  of  the  form  — /  e~  _J",  as  the  potential  of  two  mass 

points;  and  he  goes  on  to  say  that  this  formula  was  based  on 
two  assumptions,  namely  that  the  attraction  of  two  molecules 
is  inversely  as  the  square  of  the  distance,  and  second,  that  the 
universal  medium  absorbs  the  lines  of  force.  He  thus  assumes 
an  absorption  by  the  ether  of  the  attraction,  rather  than  by  a 
molecule  at  a  distance  "r."  In  his  paper  published  in  1903, 
in  which  the  real  molecular  volume,  the  value  of  "6,"  is  no 
longer  considered  constant  and  in  which  he  has  revised  his 
formula  for  the  isotherm  in  so  important  a  manner,  he  does 
not  specifically  reraise  the  question  of  the  penetration  of 
matter  by  the  cohesive  attraction. 

In  a  succession  of  papers  like  those  of  van  der  Waals' 
which  represent  a  progressive  succession  of  ideas,  mutually 
conflicting  ideas  may,  not  unnaturally,  be  found.  Thus,  in 
his  paper  on  the  thermodynamic  potential  and  capillarity,1 
a  limiting  intermediate  layer  of  rapidly  changing  density  is 
supposed  to  exist  between  the  saturated  vapor  and  the  liquid, 
and  the  existence  of  such  a  layer  would  seem  to  the  writer 
to  presuppose  that  the  radius  of  attraction  at  least  in  this 
layer  must  be  several  molecular  diameters. 

On  the  other  hand,  the  following  statement2  (p.  121)  is 
not  entirely  reconcilable  with  this  view,  and  would  be  so 
only  if  the  layers  of  which  he  speaks  are  at  least  equal  in 
thickness  to  the  distance  the  cohesive  force  extends.  He 
supposes  the  cohesive  pressure  to  be  exerted  only  by  the 
surface  layer,  but  he  states  that  exactly  the  same  formulas 
are  obtained  if  the  fluid  be  considered  to  be  made  up  of  a  series 
of  layers  of  molecular  dimensions.  "If  we  consider  the  gas  in  a 
cylindrical  vessel  of  constant  area  and  divided  into  horizontal 
layers,  the  lowest  attracts  the  next  higher,"  etc.  The  sum  of 
all  partial  amounts  of  work  will  be  the  same  as  if  one  considered 

1  Van  der  Waals:  "Theorie  thermodynamique  de  la  Capillarite,"  Archives 
Neerlandaises  des  Sciences  exactes  et  naturelles,  28,  121  (1895). 

2  Van  der  Waals :  "Die  Continuitat  des  gasformigen  u.  fliissigen  Zustandes," 
Leipzig,  p.  126  (1899). 


Relationship  between  Molecular  Cohesion  495 

only  the  attraction  of  the  upper  layer  and  the  distance  as  that 
through  which  this  layer  would  have  been  moved.  It  seems 
to  me  that,  for  this  reasoning  to  be  correct,  we  must  assume 
the  layers  at  least  as  thick  as  the  radius  of  action  of  each  layer 
of  molecules.  If  these  layers  are  of  molecular  diameters,  it 
would  seem  that  the  cohesive  force  does  not  extend  farther 
than  a  molecular  diameter.  This  is  not  apparently  con- 
sistent with  the  assumption  elsewhere  made  to  explain  the 
transitional  layer  between  vapor  and  liquid. 

Plateau  also  followed  Laplace.  Sutherland,  in  his  many 
papers  on  molecular  cohesion,  assumes  that  the  cohesional 
attraction  is  inversely  as  the  fourth  power  of  the  distance,  but 
he  does  not,  so  far  as  I  can  find,  discuss  the  question  of  the 
penetration  of  matter  by  cohesional  attraction.  But  it  is 
impossible  for  cohesion  to  vary  inversely  as  the  fourth  power, 
if  cohesion  penetrates  matter. 

Kleeman1  supposes  that  the  attraction  must  be  in- 
versely as  the  5th  or  some  higher  power  of  the  distance.  He 
has  pointed  out  that  cohesion  cannot  possibly  be  assumed  to 
vary  like  gravitation  inversely  with  the  square  of  the  distance, 
because  the  cohesional  attraction  is  so  much  greater  than 
gravitation.  But  Mills  weakened  the  force  of  this  objection, 
which  he  had  overlooked  in  his  early  papers,  by  making  the 
additional  postulate  that  cohesion  does  not  penetrate  matter. 
For  if  it  be  assumed  that  the  cohesion  does  not  penetrate 
matter  then  only  the  layer  of  superficial  molecules  of  two 
masses  would  attract  each  other;  and  the  number  of  these  is 
so  small,  compared  to  the  whole  number  of  molecules  in  the 
mass,  that  the  cohesional  attraction  would  be  less  perceptible 
at  sensible  distances  than  gravitational  attraction. 

I  have  been  unable,  then,  to  find  any  evidence  for  the 
assumption  so  generally  made  that  cohesive  attraction  pene- 
trates matter  like  gravitation.  There  is  no  direct  evidence, 
therefore,  so  far  as  I  can  find,  against  the  inference  necessitated 


1  Kleeman:  "An  Investigation  of  the  Determination  of  the  Law  of  Chemical 
Attraction  between  Atoms  from  Physical  Data,"  Phil.  Mag.,  [6]  21,  83  (1911). 


496  Albert  P.  Mathews 

by  the  square  or  fourth  power  law  of  attraction,  that  cohesion 
does  not  penetrate  matter. 

There  is,  on  the  other  hand,  some  evidence  of  a  direct  kind 
that  cohesional  attraction  extends  only  as  far  as  the  nearest 
molecules.  This  evidence  is  the  length  of  the  radius  of  action 
as  determined  by  direct  measurement,  and  Einstein's  proof 
that  the  radius  of  action  varies  with  the  distance  apart  of  the 
molecular  centers. 

Laplace  believed  that  the  radius  of  action,  although 
short,  nevertheless  extended  many  molecular  diameters  and 
this  opinion  prevailed  until  recently,  but  as  means  of  measure- 
ment have  improved  the  radius  has  shrunk.  Quincke  gave  an 
estimate  of  about  6  X  io~6  cm,  but  the  most  recent  deter- 
minations of  Johannot,1  and  Chamberlain2  show  it  to  be 
about  1.6-2  X  io~7  cm  in  a  soap  film  and  in  the  case  of  glass. 
The  diameter  of  a  molecule  of  trioleate  of  glycerine,  according 
to  Perrin,3  is  i.i  X  io~7  cm.  The  radius  of  action  is  certainly 
not  more  than  two  molecular  diameters  and  indeed  is  hardly 
more  than  one.  The  average  distance  between  the  centers 
of  two  molecules  of  ether  in  the  liquid  state  at  20°  is  about 
5.5  X  io-8cm. 

But  not  only  has  direct  measurement  shown  the  radius 
of  action  to  be  one  or  two  molecular  diameters,  but  com- 
putations of  it  by  Kleeman  make  it  very  close  to  this.  For 
example,  in  ether  Kleeman4  computed  the  radius  to  be  about 
3.4  X  io~8  cm  which  is  about  the  distance  when  the  mole- 
cules are  in  contact.  Van  der  Waals  supposed  it,  indeed,  to 
be  only  as  long  as  this.  Recently  Einstein5  has  made  a  very 
interesting  computation  starting  from  the  law  of  Eotvos,  by 
which  he  shows,  from  thermodynamic  reasoning,  that  the 

1  Johannot:  Phil.  Mag.,  [5]  47,  501  (1899). 

2  Chamberlain:  Phys.  Rev.,  31,  170  (1910). 

3  Devaux:  Journal  de  Physique,  [5]  2,  699  (1912). 

4  Kleeman:  "On  the  Radius  of  the  Sphere  of  Action,"  Phil.  Mag.,  [6]  19, 
840  (1910). 

5  Einstein:  "Bemerkung  zudemGesetz  von  Eotvos,"  Annalen  der  Physik., 
[4l  34,  165  (1911). 


Relationship  between  Molecular  Cohesion  497 

range  of  cohesive  action  must  be  of  the  general  value  of, 
and  proportional  to,  the  distance  between  the  molecular 
centers.  This  distance  is  of  the  order  of  magnitude  in  most 
liquids  of  io~8  cm.  This  result  is  so  surprising  that  Einstein 
says  of  it:  "This  result  appears  at  first  very  unlikely,  for 
what  should  the  radius  of  action  of  a  molecule  have  to  do  with 
the  distance  between  neighboring  molecules?  The  supposi- 
tion is  only  reasonable  in  case  the  neighboring  molecules  alone 
attract  each  other,  but  not  those  farther  removed. " 

Sutherland1  also  came  to  the  conclusion  that  the  radius  of 
action  was  about  equal  to  7//3.  We  see  then,  that  the  evi- 
dence points  to  the  conclusion  that  the  radius  of  action  of 
the  molecular  forces  agrees  very  closely  with  -z//3,  the  distance 
between  the  molecular  centers,  and  varies  directly  with  T//3. 
The  only  explanation  of  this  fact  appears  to  me  to  be  that  the 
attraction  does  not  extend  beyond  neighboring  molecules 
and,  hence,  must,  in  some  way,  be  stopped  by  them. 

Mills2  alone,  so  far  as  I  can  find,  has  reopened  the  question 
whether  the  field  is  delimited  by  the  surrounding  molecules. 
Concluding,  I  believe  erroneously,  from  an  empirical  law, 
that  the  attraction  between  molecules  must  vary  inversely 
as  the  square  of  the  distance,  he  was  driven  to  the  second 
conclusion  that  if  this  were  the  case  the  cohesion  could  not 
penetrate  matter.  He  assumed,  hence,  that  the  surrounding 
molecules  absorbed,  or  neutralized,  the  lines  of  cohesive  force. 
The  direct  evidence  and  Einstein's  reasoning  leaves  little 
doubt  that  the  radius  varies  with  the  distance  apart  of  the 
molecules  and  the  only  possible  conclusion  from  this  is  that 
the  surrounding  molecules  delimit  the  field  as  Mills  supposes. 
If  it  is  a  fact  that  the  surrounding  molecules  delimit  the 
field  as  the  evidence  indicates,  cohesion  is  allied  at  once  with 
magnetism,  foi"  this  is  the  very  supposition  which  Ewing 
made  to  explain  some  of  the  phenomena  of  magnetism.  Each 
molecule  of  a  ferromagnetic  substance  is  supposed  to  be  a 


1  Sutherland:  Phil.  Mag.,  [6]  4,  632,  636  (1902). 

2  Mills:  Jour.  Phys.  Chem.,  15,  417  (1911). 


498  Albert  P.  Mathews 

magnet.  In  the  non-magnetic  state  the  magnetism  of  each 
molecule  is  supposed  to  be  neutralized  by  the  surrounding 
molecules,  which  have  their  magnetic  axes  variously  directed. 
The  magnetic  field  is  thus  limited  to  a  single  molecular  diam- 
eter and  will  vary  with  the  distance  apart  of  the  molecules. 
The  magnetic  field  of  each  molecule  is  delimited  by  the  sur- 
rounding molecules.  If,  however,  these  molecules  are 
oriented,  either  by  acting  on  each  ether,  or  by  external  forces, 
then  the  magnetic  fields  coincide  and  the  magnetism  may  be 
perceived  extending  outward  from  the  mass.  In  other 
words,  to  explain  why  magnetism  does  not  persist  in  soft  iron 
and  to  account  for  magnetic  hysteresis,  Ewing  has  made 
exactly  the  same  assumption  which  has  been  made  to  explain 
why  cohesion  does  not  extend  beyond  molecular  distances. 

It  seems  to  me  not  impossible  that  magnetism  is  the 
cohesive  attraction  of  a  molecule.  If  the  molecule  is  of  such 
a  nature,  or  shape,  that  the  total  effect  of  the  little  magnets, 
its  electron  couples,  coincide  more  or  less  completely  so  that 
the  molecule  has  a  polarity,  and  the  molecules  can  be  oriented 
in  any  way  and  held  in  position,  we  have  the  ferro  and  para- 
magnetic substances.  If  the  molecules  have  many  poles,  so 
that  there  is  no  polarity  of  the  molecules  as  a  whole,  there  is  a 
diamagnetic  substance.  The  magnetic  field  of  each  molecule 
would  be  its  cohesive  field. 

The  recent  work  of  Cotton  and  Mouton1  on  the  orienta- 
tion of  molecules  in  the  magnetic  field  seems  to  me  to  bear  out 
such  an  interpretation.  The  work  of  Weiss2  and  Langevin3 
appears  to  point  in  the  same  direction,  but  Weiss,  who  has 
considered  the  possibility  of  the  identity  of  cohesion  and 
magnetism,  states  that  he  will  shortly  show  that  they  can  not 
be  identical.  Nevertheless  it  appears  to  me  not  impossible 
that  magnetism  is  simply  a  special  case  of  cohesion,  and  if 
this  is  true  the  rotation  of  the  plane  of  polarized  light  by  op- 
tically active  substances  would  be  easily  understood. 

1  Cotton  and  Mouton:  Journal  de  Physique,  [5]  I,  40  (1911). 

2  Weiss:  Journal  de  Physique,  [5]  I,  900  (1911);  [4]  6,  66 1  (1907). 

3  Langevin:  Ann.  Chim.  Phys.,  5,  70  (1905). 


Relationship  between  Molecular  Cohesion  499 

Finally,  if  it  is  true  that  the  surrounding  molecules  de- 
limit the  field  of  cohesion  in  any  way  whatever,  and  that 
only  six  molecules  really  take  part  in  this  delimitation,  we  can 
derive  the  value  a/V2  of  van  der  Waals'  at  once  and  very 
simply. 

Suppose  that  each  molecule  has  a  certain  mass  of  cohes- 
ion, M,  and  that  two  molecules  attract  each  other  directly 
as  the  product  of  their  cohesive  masses  and  inversely  as  the 
fourth  power  of  the  distance  between  their  centers,  then  the 
attraction  between  two  molecules  would  be  M2K/V/3,  where 
v  is  the  space  at  the  disposal  of  a  single  molecule.  Since 
each  molecule  attracts  only  the  one  above,  below  and  to  each 
side,  the  pressure  per  square  centimeter  of  a  double  layer  of 
molecules  will  be  M2K/V/3  multiplied  by  the  number  of  mole- 
cules in  i  sq.  cm  or  i/z>2/3,  making  M2K/7;2.  Since  the  at- 
traction extends  only  a  single  molecular  diameter,  we  may 
multiply  both  numerator  and  denominator  by  N2,  where  N 
is  the  number  of  molecules  in  the  volume,  V,  and  we  obtain, 
N2M2K/NV  -=  M2N2K/V2  ==  a/V2.  M2K  has  already  been 
shown  to  be  2.98  X  io~37  (Mol.  Wt.  X  Valences)2/3. 

We  have,  as  yet,  no  proof  that  only  the  six  surrounding 
molecules  are  attracted,  although  Sutherland1  has  made  a 
similar  supposition.  But  such  may  be  the  case  nevertheless. 
Einstein,  in  his  calculation,  computed  that  each  molecule 
could  be  considered  as  lying  at  the  center  of  a  cube  and  that 
it  attracted  the  26  other  molecules  of  the  cube.  Of  course 
the  fact  that  the  value  a/V2  may  be  so  easily  derived  in  this 
way  does  not  furnish  any  proof  that  the  attraction  is  inversely 
as  the  fourth  power  of  the  distance.  But  I  know  of  no  other 
derivation  of  a/V2  which  involves  so  few,  or  less  radical, 
assumptions. 

The  general  conclusion  of  the  paper  is  then,  that  cohesion, 

1  Sutherland :  Phil.  Mag.,  [6]  17,  667  (1909).  "The  total  potential 
energy  of  a  number  of  like  molecules  is  the  same  as  if  each  caused  its  own  domain 
to  be  uniformly  electrized  with  an  electric  moment  proportional  to  the  linear 
dimensions  of  the  domain,  the  direction  of  electrization  being  such  that  in  general 
any  molecule  attracts  its  six  immediate  neighbors." 


500  Albert  P.  Mathews 

being  a  function  of  molecular  weight  and  valence,  is  a  function 
of  the  number  of  electron  couples  of  the  valences  and  atoms, 
and  is,  hence,  probably  of  a  magnetic  nature.  Magnetic 
substances  may  be  supposed  to  be  substances  in  which,  owing 
to  the  orientation  of  the  molecules,  or  to  their  polarity,  or 
both  these  causes,  the  cohesive  fields  of  the  molecules  are  not 
delimited  or  neutralized  by  the  surrounding  molecules  so  that 
the  cohesional  attraction  becomes  apparent  at  more  than 
molecular  distances,  and  under  such  circumstances  the  sub- 
stance is  said  to  be  magnetic. 

University  of  Chicago 


THE    SIGNIFICANCE    OF    THE    RELATIONSHIP    BE- 
TWEEN MOLECULAR  COHESION  AND  THE  PROD- 
UCT OF  THE  MOLECULAR  WEIGHT  AND  THE 
NUMBER  OF  VALENCES 


BY  ALBERT  p.  MATHEWS 

In  the  preceding  papers1  of  this  series  I  have  shown  that 
the  value  of  "a"  of  van  der  Waals,  representing  molecular 
cohesion,  or  the  value  M2K  which  is  the  factor  "a"  for  a 
single  molecule,  is  proportional  to  the  two-thirds  power  of  the 
product  of  the  molecular  weight  by  the  number  of  valences 
of  the  molecule.  M2K  was  found  to  be  equal,  when  expressed 
in  absolute  units,  to  2.98  X  io~37  (Mol.  Wt.  X  No.  of  Val.)2/3. 

In  this  paper  I  shall  discuss  the  theoretical  bearing  of  the 
relationship  of  cohesion  to  these  molecular  properties. 

Attempts  have  been  made  by  others  to  correlate  cohesion, 
or  ''a,"  with  molecular  weight  and  the  number  of  valences, 
but  with  very  partial  success.  Sutherland2  at  first  supposed 
the  molecular  attraction  to  be  proportional  to  the  product 
of  the  gravitational  masses  of  the  molecules.  This  he  found 
would  not  do,  and  in  his  later  papers  he  stated  that  the  gravita- 
tional mass  of  a  molecule  did  not  enter  into  the  expression 
"a."  Amagat,3  also,  recently  revived  the  idea  that  gravita- 
tional mass  plays  a  role  in  cohesion  and  suggested  that  a/V2 
ought  to  be  proportional  to  the  square  of  the  molecular  mass. 
This,  however,  he  did  not  find  to  be  the  case.  Leduc4  has 
recently  confirmed,  in  part,  this  view  of  Amagat's  for  gases  of 
similar  molecular  composition,  when  taken  under  the  same 
volume  and  at  corresponding  temperatures.  Kleeman,5  also 
has  tried  to  find  a  relationship  between  "a"  and  gravita- 


1  Mathews:  Jour.  Phys.  Chem.,  17,  154  (1913)- 

2  Sutherland:  Phil.  Mag.,  [5]  27,  305  (1889);   [6]  4,  632  (1902). 

3  Amagat:  "Pression  interne  des  fluides,"  Journal  de  Physique,    [4]   8, 
617  (1909). 

4  Leduc:  Comptes  rendus,  153,  i?9  (I911)- 

6  Kleeman:  Phil.  Mag.,  [6]  19,  783,  840-847  (1910). 


482  Albert  P.  Mathews 

tional  mass,  and  states  that  the  cohesive  attraction  of  two 
molecules  is  proportional  to  the  product  of  the  two  sums  of 
the  square  roots  of  the  atomic  weights  of  the  atoms  of  the 
molecules.  This  relationship,  however,  is  of  very  limited 
applicability,  ifjindeed,  it  correctly  expresses  the  cohesion  of 
any. 

As  regards  valence,  I  can  find  but  one  other  suggestion, 
that  of  Sutherland.1  He  showed  that  the  number  of  equiva- 
lents, or  valences,  in  simple  substances,  such  as  sodium 
chloride,  influenced  the  value  of  their  cohesion.  He  was 
unable  to  establish  this  relationship  for  more  complex  bodies. 
Nevertheless  he  assumed  that  it  existed  in  them  and  correctly 
surmised  from  it  the  relationship  between  cohesion  and 
chemical  affinity,  and  adduced  it  as  evidence  of  the  electro- 
static or  magnetic  nature  of  cohesion,  "a"  was  made  pro- 
portional to  the  square  root  of  the  valence. 

The  relationship  between  cohesion  and  the  properties  of 
molecular  weight  and  the  number  of  valences  can  be  inter- 
preted best  by  Sir  J.  J.  Thomson's  theory  of  the  electrical 
constitution  of  matter  and  valence,  and,  so  far  as  I  can  see, 
on  no  other  hypothesis.  It  speaks,  therefore,  for  the  electro- 
static, "or  electro-magnetic  theory  of  cohesion,  and,  in  my 
opinion,  for  the  latter. 

The  relation,  M2K  =  (/)  Val2/3/Mol.  Wt.8/3,  seems  at  first 
peculiar.  It  is  odd  that  the  valence  of  an  atom  should  be  of 
as  much  importance  in  cohesion  as  the  weight  of  the  atom; 
it  is  a  relationship  which  one  would  not  have  anticipated. 
The  significance  of  this  fact,  if  I  am  not  mistaken,  is  that  the 
electron  couples  constituting  the  molecules  are  of  two  kinds, 
namely,  those  of  the  atoms  themselves,  which  added  together 
presumably  give  the  molecular  weight;  and  the  valence  elec- 
trons, which  differ  from  the  others  so  that  they  cannot  be 
added  to  them.  Hence  the  formula  is  not  M2K  =  (/)  (Wt.  + 
Val.),  the  cohesion  being  proportional  to  the  sum;  but  the 
mass  of  cohesion  is  proportional  to  the  cube  root  of  each  of 

1  Sutherland:  Phil.  Mag.,  [6]  4,  632  (1902). 


Relationship  between  Molecular  Cohesion  483 

these  kinds  of  electrons  and  so  is  proportional  to  the  cube  root 
of  their  product.  The  valence  electrons  are  probably  more 
labile,  more  easily  removed  arid  replaced.  They  have  a 
different  degree  of  liberty  and  they  cannot  be  summed  with 
the  atomic. 

The  formula  thus  confirms  the  correctness  of  Drude's 
promise  that  the  electrons  of  the  valences  differ  in  their 
properties  from  the  electrons  of  the  atoms.  He  concluded 
that  only  the  valence  electrons  would  be  sufficiently  free  to 
vibrate  synchronously  with  light  and  hence  these  electrons 
must  be  particularly  concerned  in  the  refraction  and  dis- 
persion of  light.  Drude's1  suggestion  of  electrons  of  different 
degrees  of  liberty  confirmed,  as  it  was,  by  experiments  show- 
ing a  relation  between  valence  and  dispersion,  is  thus  con- 
firmed also  from  the  wholly  different  field  of  cohesion. 

A  still  more  interesting  conclusion  may  be  drawn  from 
this  relationship,  namely,  that  a  neutral,  uncharged  atom 
having  no  valence  will  have  no  cohesion.  Since  it  will  have 
no  chemical  affinity  either,  if  chemical  affinity  is,  as  it  ap- 
pears to  be,  of  an  electrical  nature,  it  is  thus  seen  that  a  close 
relation  must  exist  between  chemical  affinity  and  cohesion. 
Such  neutral  atoms  will  presumably  still  have  gravitational 
attraction.  A  free  electrical  charge  on  the  atom  is,  therefore, 
necessary  for  cohesion,  but  not  for  gravitation.  Furthermore, 
the  cohesional  effect  is  the  same  whether  the  charge  be  positive 
or  negative;  and  it  is  proportional  to  the  number  of  charges. 
The  formula  shows,  also,  that  the  effect  of  a  free  charge  on  any 
atom  is  proportional  to  the  weight  of  the  atom;  that  is,  the 
effect  of  the  valence  charge  is  multiplied,  as  it  were,  by  the 
number  of  electron  couples  in  the  atom;  and  the  effect  of  the 
total  number  of  valence  charges  in  the  molecule  is  multiplied 
by  the  whole  number  of  atomic  electron  couples  in  the  mole- 
cule. Just  how  such  an  effect  could  be  produced,  and  why  the 
attraction,  or  cohesive  mass,  should  ultimately  prove  to  be 
proportional  to  a  linear  function  (the  cube  root)  of  the  product 


1  Drude:  Annalen  der  Physik.,  [4]  14,  677  (1904). 


484  Albert  P.  Mathews 

of  the  number  of  valences  by  the  molecular  weight,  I  do  not 
see. 

It  appears,  then,  that  refraction,  dispersion  and  cohesion 
all  involve  the  valence  electrons,  but  the  connection  between 
cohesion  and  valence  is  far  closer  and  simpler  than  the  other 
relationships  appear  to  be.  The  relationship  of  valence  to 
light  is  necessarily  a  less  direct  one,  refraction  depending 
on  the  rate  of  vibration  of  the  electron.  It  is  said1  that  if  the 
natural  period  of  the  molecule  (electron)  is  slightly  less  than 
the  frequency  of  a  light  wave  the  light  will  be  accelerated; 
if  greater,  retarded.  It  is  evident  that  in  dispersion  other 
properties  of  the  electrons  than  number  come  into  play,  and, 
hence,  the  relationship  between  dispersion  and  number  is 
not  so  simple  and  direct.  Double  bonds,  neighboring  groups, 
etc.,  influence  the  periods  of  the  electrons  and  so  influence  the 
dispersive  power;  whereas  these  factors  appear  to  play  no 
important  part  in  cohesion. 

The  relation  between  the  refraction  of  light  of  one  wave 
length  and  the  valence  number  is  still  less  direct  than  be- 
tween dispersion  and  valence,  but  still  a  general  relation 
exists  which  for  substances  of  the  same  type  is  rather  uniform, 
as  shown  by  Traube2  for  many  liquids  and  by  Cuthbertson3 
for  several  gases. 

Another  very  interesting  fact  correlating  the  refractive  and 
cohesive  properties  of  matter  is  the  resemblance  between  the 
constant  "K"  of  the  Ketteler  dispersion  formula  and  the 
value  M2K  of  cohesion.  Thus  with  the  Ketteler  formula 
n*  =  a2  --  K  P  +  D  X\/(P  —  X\)  the  constant  "K,"  Drude 
found,  could  be  computed  with  a  fair  approximation,  in  some 
cases  at  any  rate,  from  the  sum  of  the  valences,  the  molecular 
weight  and  the  density,  and  this  result  was  confirmed  by 
Erfle.4  This  constant  "K,"  therefore,  contains  at  least 

1  Cotter,  J.  R.:  "Dispersion,"  Encyclo.  Brit.,  nth  edition,  8,  317. 

2  Traube:  Ber.  chem.  Ges.  Berlin,  40,  130  (1907). 

3  Cuthbertson:  Proc.  Roy.  Soc.,  8aA  (1909-1910);  Phil.  Mag.,   [6]  21,  69 
(1911);  Phil.  Trans.,  204,  323  (1905);  207,  135  (1907). 

4  Erfle:  "Optische  Eigenschaften  und  Elektronen  Theprie."    Annalen  der 
Physik,  [4]  24  (1907). 


Relationship  between  Molecular  Cohesion  485 

sometimes  the  same  factors  as  the  value  a/V2  of  van  der 
Waals'  equation.  I  have  not,  however,  attempted  to  estab- 
lish any  closer  connection  between  them.1 

We  conclude,  therefore,  that  while  cohesion  and  re- 
fractivity  are  both  dependent  on  a  common  factor,  namely 
the  valence  electrons,  and  possibly  upon  the  molecular  weight, 
the  connection  between  them  is  not  direct,  but  indirect; 
and  while  cohesion  and  refraction,  or  dispersion,  often  parallel 
each  other,  they,  at  other  times,  diverge  considerably  since 
other  factors  enter  into  refraction. 

It  is  not  without  interest  to  recall  as  an  example  of  the 
perspicacity  of  genius,  that  Laplace2  long  ago  foretold  a  con- 
nection between  these  properties.  Writing  in  1805  of  the 
formula  of  capillarity  which,  as  will  be  remembered,  con- 
tained two  terms,  one  K,  representing  molecular  cohesion, 
or  van  der  Waals'  expression  a/V;  the  other,  H,  the  capillary 
constant,  Laplace  says  (p.  351):  "I  saw  that  this  action 
(pressure)  is  smaller  or  larger  than  if  the  surface  is  plane; 
smaller,  if  the  surface  is  concave;  larger,  if  it  is  convex.  Its 
analytical  expression  is  composed  of  two  terms:  the  first 
(K),  much  larger  than  the  second,  expresses  the  action  of  the 
mass  terminated  by  a  plane  surface;  and  I  think  from  this 
term  depends  the  suspension  of  mercury  in  a  barometer  tube 
at  a  height  two  to  three  times  greater  than  that  due  to 
atmospheric  pressure,  the  refractive  powers  of  diaphanous 
bodies,  the  cohesion,  and  in  general,  chemical  affinity;  the 
second  term  expresses  the  part  of  the  action  due  to  the  spheri- 
city of  the  surface."  And  again  (p.  362) :  "The  function,  K, 
is  analogous  to  that  I  have  designated  by  the  same  letter  in 
the  refraction  of  light." 

But  of  even  greater  interest  and  more  fundamental 
importance  than  the  relation  between  the  optical  and  the 
cohesive  properties,  which  is  now  understandable  since  both 


1  See  also  Natanson:  Bull,  de  1'Acad.  des  Sci.  de  Cracovie,  1907,  April 
p.  316  for  the  relation  of  refraction  and  valence. 

2  Laplace:   Sur  1'action   capillaire.   Oeuvres.   Supp.    Liv.   X,   Traite  de 
Mecanique  Celeste,  p.  351. 


486  Albert  P.  Mathews 

involve  the  number  of  valence  electrons,  is  the  relation  be- 
tween the  magnetic  and  cohesive  properties,  since  here  we 
touch,  I  think,  the  very  kernel  of  the  problem  of  the  nature 
of  cohesion. 

The  connection  between  the  magnetic  properties  and 
cohesion  is  brought  out  very  clearly,  in  an  empirical  way, 
by  Pascal's1  investigations  on  the  relation  between  magnetic 
susceptibility  and  the  molecular  properties.  In  a  series  of 
papers  Pascal  has  shown  that  there  is  a  remarkable  con- 
nection between  the  specific  susceptibility  of  diamagnetic 
elements  and  the  atomic  weights  and  valences.  Thus  if 
elements  of  the  same  family  having  the  same  valence  are 
arranged  in  their  order  of  increasing  specific  susceptibility, 
they  are  in  the  order  of  their  atomic  weights;  and,  on  the 
other  hand,  a  close  dependence  on  valence  may  be  observed. 
In  elements  of  nearly  the  same  weight  but  of  different  valence 
numbers,  the  atomic  magnetic  susceptibility,  Xa,  increases 
with  the  number  of  valences.  An  empirical  relationship 
was  found  between  them,  Xa  —  io~7ea  +  l*a  where  a  is 

about  2.1,  /?  about  0.004  and  a  the  atomic  weight,  a  and  p 
depend  only  on  valence.  But  here,  also,  double  bonds  made 
their  effect  felt,  though  less  pronouncedly  than  in  refraction. 
Double  bonded  molecules  have,  in  general,  a  lower  molecular 
susceptibility  than  that  calculated.  Other  effects  of  molecular 
form  are  seen;  for  example,  the  benzene  nucleus  augments 
the  diamagnetism,  although  the  double  bonds  it  is  supposed 
to  contain  should  have  an  opposite  effect.  The  factor  of 
molecular  structure  appears,  then,  to  influence  diamagnetism. 
On  the  whole,  however,  calculation  of  the  number  of  valences 
in  the  molecule  by  this  procedure  agrees  better  with  the  calcu- 
lation from  the  cohesion,  than  does  the  calculation  from  the 
refractivity  or  dispersion.  Thus,  double  bonds  are  of  less 
action  on  the  diamagnetism  and  in  the  benzene  nucleus  they 


1  Pascal :  "Sur  im  mode  de  contr61e  optique  des  analyses  magne"  tochimiques, ' ' 
Comptes  rendus,  152,  1852  (1911).  Recherches  magne to-chimiques  sur  la  struc- 
ture atomique  des  halogenes,"  Comptes  rendus,  152,  826  (1911).  Ann.  Chim. 
Phys.,  [8]  19,  1-80  (1910). 


Relationship  between  Molecular  Cohesion  487 

appear  to  exert  no  effect.  By  this  method,  as  by  the  cohesional, 
all  organic  chlorine  compounds  examined  were  found  to  have 
trivalent  chlorine  and  fluorine  was  monovalent.  The  agree- 
ment was  good  in  regard  to  other  elements  also. 

The  connection  between  cohesion  and  diamagnetism  is, 
therefore,  again  an  indirect  one.  Both  involve  the  molecular 
weight  and  the  number  of  valences,  but  it  is  clear  that  cohesion 
is  independent  of  molecular  form,  or  very  largely  so;  whereas 
whether  a  substance  is  magnetic,  or  diamagnetic,  may  depend, 
in  part  upon  this  very  factor.  Oxygen  in  an  elemental  form, 
is  paramagnetic,  not  diamagnetic,  and  is  quite  anomalous  in 
Pascal's  scheme;  whereas  the  cohesion  of  oxygen  is  not  anomal- 
ous. In  other  words,  whether  a  body  is,  as  a  whole,  para- 
magnetic or  diamagnetic,  and  to  what  degree,  depends,  prob- 
ably, on  the  possibility  of  the  orientation  of  the  molecules, 
their  polarity,  etc.,  factors  which  do  not  seem  to  affect  their 
cohesion  or  gravitation.  Nevertheless  cohesion  and  magnetic 
properties  are,  no  doubt,  closely  related,  since  both  depend 
on  the  same  molecular  properties,  only  magnetism  involves 
still  other  properties,  (form)  not  involved  in  cohesion. 

The  fact  that  cohesion  is  thus  determined  fry  the  number 
of  electron  couples  (atomic  and  valence)  in  the  molecule 
plainly  points  toward  the  conclusion  that  cohesion  is  either 
electro-static  or  electro-magnetic  in  nature.  Both  of  these 
possibilities  have  already  been  suggested.  Sutherland,1  from 
his  discovery  of  the  relation  of  cohesion  to  valence  in  salts, 
inferred  at  first  that  the  cohesion  must  be  of  an  electromagnetic 
nature.  He  supposed  these  rotating  electron  couples  acted 
like  little  magnets,  and  he  attempted  to  show,  though  whether 
successfully,  or  not,  I  am  unable  to  judge,  that  small  magnets, 
at  sufficient  distances  apart,  would  attract  inversely  as  the 
fourth  power  of  the  distance  between  them,  and  this  he  sup- 
posed to  be  the  law  of  molecular  attraction.  This  conclusion 
was  attacked  by  van  der  Waals,  Jr.,2  who  concluded,  also 

1  Sutherland:  Phil.  Mag.,  [6]  19,  i  (1910);  4,  625  (1902). 

2  Van  der  Waals,   Jr. :  Kon.   Akad.   v.   Wetensch.   te  Amsterdam,   Pro- 
ceedings, n,  132  (1908-1909). 


488  Albert  P.  Mathews 

from  mathematical  reasoning,  that  the  attraction  between 
such  magnets  would  be  inversely  as  the  yth  or  9th  power  of 
the  distance,  and  thus  agree  with  the  assumptions  of  his  father, 
that  molecular  attraction  diminished  at  such  a  rate  that  it 
was  effective  only  when  the  molecules  were  in  contact.  lyater, 
Sutherland1  concluded  that  cohesional  attraction  was  due  to 
electrostatic  affinity  of  these  electron  couples.  Lodge2  made 
a  similar  suggestion.  He  thought  some  of  the  lines  of  force 
between  the  atoms  wandered  outside  the  molecule  to  atoms  of 
other  molecules  and  thus  produced  molecular  cohesion.  This 
would  make  molecular  cohesion  of  the  same  nature  as  chemical 
affinity.  While  the  relation  between  the  two  is  close,  both 
being  zero  in  the  absence  of  an  electric  charge,  or  valence, 
one  is  not  causally  dependent  on  the  other,  although  both 
depend  on  the  valences.  The  attraction  between  the  atoms 
is  probably  of  an  electrostatic  kind  and,  if  so,  should  vary 
inversely  as  the  square  of  the  distance.  The  atomic  weight 
does  not  appear  to  play  a  part  in  chemical  affinity,  for  very 
light  elements  may  enter  into  very  firm  union.  In  cohesion, 
molecular  weight  does  play  a  large  part;  and  while  it  is  not 
impossible  that  the  cohesional  attraction  may  be  inversely 
as  the  square  of  the  distance,  it  is  not  probable,  or  at  any 
rate  it  has  not  yet  been  proved  to  general  satisfaction. 

It  seems  much  more  probable  to  me  that  cohesion  is  more 
closely  related  to  magnetism  than  to  electrostatic  affinity 
and  I  would  raise  the  question  whether  magnetism  is  anything 
else  than  molecular  cohesion  made  apparent  at  distances 
more  than  molecular.  Is  it  not  possible  that  molecular  cohe- 
sion, involving  as  it  does  both  atomic  and  valence  electrons 
(atomic  weight  and  valence)  is  due,  perhaps,  to  the  magnetic 
effects  produced  by  the  movements  of  these  electron  couples? 
In  this  view  the  atoms  would  be  united  by  their  electro- 
static affinities  and  these  same  valences  and  the  other  atomic 
electrons  by  their  magnetic  effects  produce  the  molecular 


1  Sutherland:  Phil.  Mag.,  [6]  17,  667  (1909). 

2  Lodge:  Nature,  70,  176  (1904). 


Relationship  between  Molecular  Cohesion  489 

cohesion.  I  may  state  briefly  some  of  the  reasons  which  ap- 
pear to  lead  to  such  a  conclusion. 

In  the  first  place  we  have  the  surprising  fact  that  the 
field  of  cohesion  of  a  molecule  is  apparently  delimited  by 
the  surrounding  molecules.  The  evidence  for  this,  while 
perhaps  not  conclusive,  is  both  direct  and  indirect.  The 
reason  for  the  shortness  of  the  radius  of  action  of  cohesion  is 
one  of  the  most  interesting  questions  of  molecular  physics. 
It  is  of  interest  to  see  how  this  question  came  to  be  generally 
considered  closed  and  settled  in  favor  of  the  view,  now  gener- 
ally accepted,  that  cohesional  attraction  diminishes  with  the 
distance  at  a  rate  far  greater  than  gravitational  attraction. 
It  is  chiefly  due  to  Laplace. 

Laplace,1  in  his  beautiful  memoir  on  capillarity,  first 
raised  the  question  whether  the  short  radius  of  attraction 
of  the  cohesive  forces  was  due  to  the  fact  that  matter  shut 
off  the  attraction,  or  was  due  to  the  attraction  diminishing 
with  the  distance  at  a  rate  far  more  rapid  than  gravitation. 

He  says,  when  discussing  Hawksbee's  well-known  ex- 
periments proving  that  the  height  to  which  water  rises  in  a 
glass  tube  is  independent  of  the  thickness  of  the  wall  of  the 
tube:  "Hawksbee  a  observe  que  dans  les  tubes  de  verre, 
ou  tres  minces  ou  tres  epais,  1'eau  s'elevait  a  la  meme  hauteur 
toutes  les  fois  que  les  diametres  interieurs  etaient  les  memes. 
Les  couches  cylindriques  du  verre  qui  sont  a  une  distance 
sensible  de  la  surface  interieure  ne  contribuent  done  point  a 
1' ascension  de  1'eau,  quoique  dans  chacune  d'elles,  prise 
separement,  ce  fluide  doive  s'elever  au-dessus  du  niveau. 
Ce  n'est  point  1'interposition  des  couches  qu'elles  embrassent 
qui  arrete  leur  action  sur  1'eau,  car  il  est  naturel  de  penser 
que  les  attractions  capillaires  se  transmettent  a  tracers  les  corps, 
ainsi  que  la  pesanteur;  cette  action  ne  disparait  done  qu'a  raison 
de  la  distance  du  fluide  a  ces  couches,  d'ou  il  suit  que  V attraction 
du  uerre  sur  Veau  n'est  sensible  qu'a  des  distances  insensibles ." 
I  have  italicized  the  end  of  Laplace's  statement  to  bring  out 

1  Laplace:  "Sur  1'action  capillaire.  Oeuvres.  Supp.  au  Livre  X,"  Traite  de 
Mecanique  Celeste,  p.  351;  see  also  p.  487. 


490  Albert  P.  Mathews 

clearly  the  reason  which  led  him  to  the  conclusion  that  molecu- 
lar cohesion  penetrated  matter  like  gravitation,  and  that  the 
attraction  must,  hence,  decrease  very  rapidly  with  the  dis- 
tance. It  will  be  seen  that  the  sole  reason  for  his  decision 
was  the  possible  analogy  between  gravitation  and  molecular 
cohesion. 

The  very  important  result  of  the  rejection  by"  Laplace 
of  the  possibility  of  cohesive  attraction  not  penetrating  matter 
was  that  it  forced  him  to  the  conclusion  that  the  cohesive 
force  must  diminish  far  more  rapidly  than  gravitation  as  the 
distance  increases.  Laplace  did  not  make  any  assumption 
as  to  the  rate  at  which  the  cohesional  attraction  diminished 
with  the  distance,  except  that  it  was  at  so  rapid  a  rate  that 
the  cohesion  became  negligible  within  all  measurable  dis- 
tances. 

The  great  English  philosopher-,  Thomas  Young,1  who 
a  year  before  Laplace  had  shown  the  true  nature  of  surface 
tension  and  practically  anticipated  all  of  Laplace's  main 
conclusions,  does  not  appear  to  have  raised  the  question  in 
a  concrete  form.  His  papers  on  capillarity  are  so  condensed 
that  the  reasoning  is  very  difficult  to  follow.2 

But  while  Young  nowhere  specifically  puts  the  question 
whether  the  cohesional  attraction  penetrates  matter,  he 
made  an  assumption  which  might  be  taken  to  indicate  that 
it  does  not.  ''We  may  suppose,"  he  says  (p.  43),  "the  parti- 
cles of  liquids,  and  probably  those  of  solids  also,  to  possess 
that  power  of  repulsion  which  has  been  demonstratively 
shown  by  Newton  to  exist  in  aeriform  fluids,  and  which  varies 
as  the  simple  inverse  ratio  of  the  distance  of  the  particles 
from  each  other.  In  air  and  vapors  this  force  appears  to  act 


1  Young:  "An   Essay  on   the   Cohesion   of   Fluids,"    Phil.    Trans.,    1805 
(collected  works,  edited  by  G.  Peacock,  i,  418  (1855),  London). 

2  A  propos  of  this  paper  of  Young's,  Clerk  Maxwell  makes  an  interesting 
comment.     He  says:  "His    [Young's]  essay  contains  the  solution  of  a  great 
number  of  cases  including  most  of  those  afterwards  solved  by  Laplace;  but  his 
methods  of  demonstration,  though  always  correct  and   often  extremely  elegant, 
are  sometimes  rendered  obscure  by  his  scrupulous  avoidance  of  mathematical 
symbols."     Ency.  Brit.,  Article,  "Capillarity." 


Relationship  between  Molecular  Cohesion  491 

uncontrolled;  but  in  liquids  it  is  overcome  by  a  cohesive  force, 
while  the  particles  still  retain  a  power  of  moving  freely  in  all 
directions;  and  in  solids  the  same  cohesion  is  accompanied 
by  a  stronger  or  weaker  resistance  to  all  lateral  motion,  which 
is  perfectly  independent  of  the  cohesive  force  and  which  must 
be  cautiously  distinguished  from  it."  "It.  is  sufficient  to 
suppose  the  force  of  cohesion  nearly  or  perfectly  constant  in  its 
magnitude  throughout  the  minute  distance  to  which  it  extends, 
and  owing  its  apparent  diversity  to  the  contrary  action  of 
the  repulsive  force,  which  varies  with  the  distance.  Now, 
in  the  internal  parts  of  a  liquid,  these  forces  hold  each  other 
in  a  perfect  equilibrium,  the  particles  being  brought  so  near 
that  the  repulsion  becomes  precisely  equal  to  the  cohesive 
force  that  urges  them  together,"  etc. 

Young  thus  assumed  that  the  cohesion  extended  but 
a  short  distance,  with  slight  variation  in  intensity  and  that 
it  then  ended  abruptly.  So  far  as  I  can  find,  he  made  no 
suggestion  how  it  came  to  end  abruptly;  but  if  it  be  assumed 
that  it  does  not  penetrate  matter,  it  is  seen  that  it  must  end 
abruptly  at  the  next  layer  of  molecules.  Young  tried  to  esti- 
mate how  far  the  cohesive  force  really  extended,  and  found  a 
value  surprisingly  near  the  order  of  magnitude  of  that  now 
known  to  be  the  distance  apart  of  the  centers  of  two  molecules. 
His  reasoning  on  this  point  is  extremely  ingenious,  and  is 
of  interest  as  the  first  estimate  of  molecular  dimensions. 

Lord  Rayleigh1  says  anent  this  computation  of  Young's: 
"One  of  the  most  remarkable  features  of  Young's  treatise  is 
his  estimate  of  the  range  "a"  of  the  attractive  force  on  the 
basis  of  the  relation  T  =  Y3aK.  Never  once  have  I  seen  it 
alluded  to,  and  it  is,  I  believe,  generally  supposed  that  the 
first  attempt  of  this  kind  is  not  more  than  twenty  years  old. 
It  detracts  nothing  from  the  merit  of  this  wonderful  specu- 
lation that  a  more  precise  calculation  does  not  verify  the 
numerical  coefficient  in  Young's  equation.  The  point  is 

1  Rayleigh:  "On  the  Theory  of  Surface  Forces,"  Phil.  Mag.,  [5]  30,  285-298, 
456-475  (1890).     Collected  papers,  3i  396. 


492  Albert  P.  Mathews 

that  the  range  of  the  cohesive  forces  is  necessarily  of  the 
order  T/K."  T  is  the  surface  tension  and  K  the  internal 
pressure.  Lord  Rayleigh,  in  his  revision  of  Maxwell's  classical 
account  of  capillarity  in  the  new  edition  of  the  Encyclopaedia 
Britannica  and  in  his  many  splendid  writings  on  this  subject, 
does  not  seem  .to  have  considered  this  question.  All  other 
writers  whom  I  have  consulted  seem  to  have  followed  Laplace's 
lead  and  assumed,  without  evidence,  that  cohesion  does 
penetrate  matter  like  gravitation. 

Thus,  Gauss,1  who  introduced  clear  ideas  of  surface 
energy  and  the  potential  energy  of  fluids,  writes  as  follows 
in  1830:  "The  ordinary  attraction  which  is  proportional 
to  the  square  of  the  distance,  and  which  permits  the  repre- 
sentation of  all  motions  in  the  heavens  with  such  good  agree- 
ment, can  be  used  in  the  explanation  neither  of  capillary 
phenomena  nor  of  adhesion  and  cohesion;  a  correctly  carried 
out  computation  shows  'dass  eine  nach  diesem  Gesetze  wirk- 
ende  Anziehung  eines  beliebigen  Korpers  der  zur  Ausfiihrung 
von  Experimenten  geeignet  ist,  d.  h.,  dessen  Masse  im  Ver- 
gleich  mit  der  der  Erde  vernachlassigt  werden  kann,  auf 
einem  beliebig  gelegenen,  sogar  den  Korper  beruhrenden 
Punkt,  im  Vergleich  mit  der  Schwere  verschwinden  muss. 
Wir  schliessen  hieraus  dass  jenes  Anziehungsgesetz  in  den 
kleinsten  Abstanden  mit  der  Wahrheit  nicht  mehr  uberein- 
stimmt,  sondern  dass  es  eine  Mgdification  erfordert. '  In 
other  words,  the  particles  of  the  body  exert,  besides  the  at- 
tractive force  of  gravitations,  still  another  force  which  is  notice- 
able only  in  the  smallest  distances.  All  appearances  show 
uniformly  that  the  second  part  of  the  attractive  force  (the 
molecular  attraction)  is  not  noticeable  in  the  smallest  meas- 
urable distances.  On  the  other  hand,  in  unmeasurably  small 
distances  it  may  greatly  surpass  the  first,  which  is  propor- 
tioned to  the  square  of  the  distance. 


1  Gauss:  "Allgemeine  Grundlagen  einer  Theorie  der  Gestalt  von  Fliis- 
sigkeiten,"  Ostwald's  "Klassiker  der  exakten  Wissenschaften,"  No.  135,  p.  i. 
"Corrrmentationes  societatis  Regiae  Scientiarium  Gottingensis  Recentiores,"  vii, 
1830. 


Relationship  between  Molecular  Cohesion  493 

It  was  necessary  for  him  (p.  21),  to  make  some  assump- 
tions regarding  the  cohesional  attraction  which  he  represented 
as  "/"  (r),  r  being  the  radius  of  molecular  action,  and  he 
accordingly  adopted  Laplace's  view  that  /  (r)  decreases  far 
more  rapidly  than  i/r2,  which  is  the  law  of  gravitational 
attraction  (p.  22).  He  says,  speaking  of  cohesional  attrac- 
tion, or  /  (r) :  "Da  dieser  Ausdruck  etwas  unbestimmtes 
hat  so  lange  wir  nicht  eine  Einheit  zu  Grunde  legen,  wollen 
wir  vor  allem  darauf  aufmerksam  machen,  dass  wir  die  anzie- 
hende  Kraft  /  (r),  ausgedruckt  als  eine  Function  des  Abstandes 
r,  mit  einer  Masse  multipliziert  denken  mussen,  damit  sie 
mit  der  Gravitation  g  in  den  Dimensionen  ubereinstimmt. 
Der  Sinn  unserer  Voraussetzung  ist  dann  der  folgende :  Bezeich- 
net  M  irgend  eine  Masse  derart,  wie  sie  uns  in  Experimenten 
vorkommt,  namlich  eine,  die  im  Vergleich  mit  der  ganzen 
Erde  als  verschwindend  angesehen  werden  kann,  dann  muss 
M  /  (r)  immer  merklich  sein  im  Vergleich  mit  der  Schwere, 
so  lange  r  einen  unseren  Messungen  zuganglichen,  wenn  auch 
noch  so  kleinen  Wert  hat." 

Van  der  Waals,  in  all  his  earlier  writings,  including  his 
famous  essay  on  the  continuity  of  the  gaseous  and  liquid 
states  published  in  1869,  assumed  with  Laplace  that  molec- 
ular cohesion  was  appreciable  only  very  close  to  the  molecule; 
indeed,  the  radius  of  action  was  less  than  the  mean  distance 
apart  of  the  molecular  centers.  I  have  not  been  able  to  find 
in  his  essays  any  specific  discussion  of  the  question  whether 
cohesional  attraction  penetrates  matter,  although  he  does 
discuss  the  radius  of  attraction  of  a  molecule.1  His  general 
assumption  was  that  the  cohesion  diminished  very  rapidly 
as  the  molecules  separated.  In  one  brief  communication  to 
the  Amsterdam  Academy  of  Sciences  (1893-94,  pp.  20-21)  he 
states  that  he  had  derived  a  potential  function,  that  is,  a 
function  expressing  the  potential  energy  of  attraction  of  two 


1  Van  der  Waals:  "Bijdrage  tot  de  Kennis  van  de  Wet  der  Overeenstem- 
mende  Toestanden,"  Verhandelingen  Konik.  Akad.  van  Wettenschappen,  21,  5 
(1881). 


494  Albert  P.  Mathews 

r 

molecules,  of  the  form  — /  e * ,  as  the  potential  of  two  mass 

,    r 

points;  and  he  goes  on  to  say  that  this  formula  was  based  on 
two  assumptions,  namely  that  the  attraction  of  two  molecules 
is  inversely  as  the  square  of  the  distance,  and  second,  that  the 
universal  medium  absorbs  the  lines  of  force.  He  thus  assumes 
an  absorption  by  the  ether  of  the  attraction,  rather  than  by  a 
molecule  at  a  distance  "r."  In  his  paper  published  in  1903, 
in  which  the  real  molecular  volume,  the  value  of  "6,"  is  no 
longer  considered  constant  and  in  which  he  has  revised  his 
formula  for  the  isotherm  in  so  important  a  manner,  he  does 
not  specifically  reraise  the  question  of  the  penetration  of 
matter  by  the  cohesive  attraction. 

In  a  succession  of  papers  like  those  of  van  der  Waals' 
which  represent  a  progressive  succession  of  ideas,  mutually 
conflicting  ideas  may,  not  unnaturally,  be  found.  Thus,  in 
his  paper  on  the  thermodynamic  potential  and  capillarity,1 
a  limiting  intermediate  layer  of  rapidly  changing  density  is 
supposed  to  exist  between  the  saturated  vapor  and  the  liquid, 
and  the  existence  of  such  a  layer  would  seem  to  the  writer 
to  presuppose  that  the  radius  of  attraction  at  least  in  this 
layer  must  be  several  molecular  diameters. 

On  the  other  hand,  the  following  statement2  (p.  121)  is 
not  entirely  reconcilable  with  this  view,  and  would  be  so 
only  if  the  layers  of  which  he  speaks  are  at  least  equal  in 
thickness  to  the  distance  the  cohesive  force  extends.  He 
supposes  the  cohesive  pressure  to  be  exerted  only  by  the 
surface  layer,  but  he  states  that  exactly  the  same  formulas 
are  obtained  if  the  fluid  be  considered  to  be  made  up  of  a  series 
of  layers  of  molecular  dimensions.  "If  we  consider  the  gas  in  a 
cylindrical  vessel  of  constant  area  and  divided  into  horizontal 
layers,  the  lowest  attracts  the  next  higher,"  etc.  The  sum  of 
all  partial  amounts  of  work  will  be  the  same  as  if  one  considered 


1  Van  der  Waals:  "Theorie  thermodynamique  de  la  Capillarite,"  Archives 
Neerlandaises  des  Sciences  exactes  et  naturelles,  28,  121  (1895). 

2  Van  der  Waals:  "Die  Continuitat  des  gasformigen  u.  flussigen  Zustandes," 
Leipzig,  p.  126  (1899). 


Relationship  between  Molecular  Cohesion  495 

only  the  attraction  of  the  upper  layer  and  the  distance  as  that 
through  which  this  layer  would  have  been  moved.  It  seems 
to  me  that,  for  this  reasoning  to  be  correct,  we  must  assume 
the  layers  at  least  as  thick  as  the  radius  of  action  of  each  layer 
of  molecules.  If  these  layers  are  of  molecular  diameters,  it 
would  seem  that  the  cohesive  force  does  not  extend  farther 
than  a  molecular  diameter.  This  is  not  apparently  con- 
sistent with  the  assumption  elsewhere  made  to  explain  the 
transitional  layer  between  vapor  and  liquid. 

Plateau  also  followed  Laplace.  Sutherland,  in  his  many 
papers  on  molecular  cohesion,  assumes  that  the  cohesional 
attraction  is  inversely  as  the  fourth  power  of  the  distance,  but 
he  does  not,  so  far  as  I  can  find,  discuss  the  question  of  the 
penetration  of  matter  by  cohesional  attraction.  But  it  is 
impossible  for  cohesion  to  vary  inversely  as  the  fourth  power, 
if  cohesion  penetrates  matter. 

Kleeman1  supposes  that  the  attraction  must  be  in- 
versely as  the  5th  or  some  higher  power  of  the  distance.  He 
has  pointed  out  that  cohesion  cannot  possibly  be  assumed  to 
vary  like  gravitation  inversely  with  the  square  of  the  distance, 
because  the  cohesional  attraction  is  so  much  greater  than 
gravitation.  But  Mills  weakened  the  force  of  this  objection, 
which  he  had  overlooked  in  his  early  papers,  by  making  the 
additional  postulate  that  cohesion  does  not  penetrate  matter. 
For  if  it  be  assumed  that  the  cohesion  does  not  penetrate 
matter  then  only  the  layer  of  superficial  molecules  of  two 
masses  would  attract  each  other;  and  the  number  of  these  is 
so  small,  compared  to  the  whole  number  of  molecules  in  the 
mass,  that  the  cohesional  attraction  would  be  less  perceptible 
at  sensible  distances  than  gravitational  attraction. 

I  have  been  unable,  then,  to  find  any  evidence  for  the 
assumption  so  generally  made  that  cohesive  attraction  pene- 
trates matter  like  gravitation.  There  is  no  direct  evidence, 
therefore,  so  far  as  I  can  find,  against  the  inference  necessitated 


1  Kleeman:  "An  Investigation  of  the  Determination  of  the  Law  of  Chemical 
Attraction  between  Atoms  from  Physical  Data,"  Phil.  Mag.,  [6]  21,  83  (1911). 


496  Albert  P.  Mathews 

by  the  square  or  fourth  power  law  of  attraction,  that  cohesion 
does  not  penetrate  matter. 

There  is,  on  the  other  hand,  some  evidence  of  a  direct  kind 
that  cohesional  attraction  extends  only  as  far  as  the  nearest 
molecules.  This  evidence  is  the  length  of  the  radius  of  action 
as  determined  by  direct  measurement,  and  Einstein's  proof 
that  the  radius  of  action  varies  with  the  distance  apart  of  the 
molecular  centers. 

Laplace  believed  that  the  radius  of  action,  although 
short,  nevertheless  extended  many  molecular  diameters  and 
this  opinion  prevailed  until  recently,  but  as  means  of  measure- 
ment have  improved  the  radius  has  shrunk.  Quincke  gave  an 
estimate  of  about  6  X  io~6  cm,  but  the  most  recent  deter- 
minations of  Johannot,1  and  Chamberlain2  show  it  to  be 
about  1.6-2  X  io~7  cm  in  a  soap  film  and  in  the  case  of  glass. 
The  diameter  of  a  molecule  of  trioleate  of  glycerine,  according 
to  Perrin,3  is  i.i  X  io~7  cm.  The  radius  of  action  is  certainly 
not  more  than  two  molecular  diameters  and  indeed  is  hardly 
more  than  one.  The  average  distance  between  the  centers 
of  two  molecules  of  ether  in  the  liquid  state  at  20°  is  about 
5.5  X  io-8cm. 

But  not  only  has  direct  measurement  shown  the  radius 
of  action  to  be  one  or  two  molecular  diameters,  but  com- 
putations of  it  by  Kleeman  make  it  very  close  to  this.  For 
example,  in  ether  Kleeman4  computed  the  radius  to  be  about 
3.4  X  io~8  cm  which  is  about  the  distance  when  the  mole- 
cules are  in  contact.  Van  der  Waals  supposed  it,  indeed,  to 
be  only  as  long  as  this.  Recently  Einstein5  has  made  a  very 
interesting  computation  starting  from  the  law  of  Eotvos,  by 
which  he  shows,  from  thermodynamic  reasoning,  that  -the 


1  Johannot:  Phil.  Mag.,  [5]  47,  501  (1899). 

2  Chamberlain:  Phys.  Rev.,  31,  170  (1910). 


3  Devaux:  Journal  de  Physique,  [5]  2,  699  (1912). 

4  Kleeman:  "On  the  Radius  of  the  Sphere  of  Action,"  Phil.  Mag.,  [6]  19, 
840  (1910). 

8  Einstein:  "Bemerkung  zu  dem  Gesetz  von  Eotvos,"  Annalen  der  Physik., 
[4]  34,  165  (19-11). 


Relationship  between  Molecular  Cohesion  497 

range  of  cohesive  action  must  be  of  the  general  value  of, 
and  proportional  to,  the  distance  between  the  molecular 
centers.  This  distance  is  of  the  order  of  magnitude  in  most 
liquids  of  io~8  cm.  This  result  is  so  surprising  that  Einstein 
says  of  it:  "This  result  appears  at  first  very  unlikely,  for 
what  should  the  radius  of  action  of  a  molecule  have  to  do  with 
the  distance  between  neighboring  molecules?  The  supposi- 
tion is  only  reasonable  in  case  the  neighboring  molecules  alone 
attract  each  other,  but  not  those  farther  removed. " 

Sutherland1  also  came  to  the  conclusion  that  the  radius  of 
action  was  about  equal  to  i//3.  We  see  then,  that  the  evi- 
dence points  to  the  conclusion  that  the  radius  of  action  of 
the  molecular  forces  agrees  very  closely  with  v1/8,  the  distance 
between  the  molecular  centers,  and  varies  directly  with  -z//3. 
The  only  explanation  of  this  fact  appears  to  me  to  be  that  the 
attraction  does  not  extend  beyond  neighboring  molecules 
and,  hence,  must,  in  some  way,  be  stopped  by  them. 

Mills2  alone,  so  far  as  I  can  find,  has  reopened  the  question 
whether  the  field  is  delimited  by  the  surrounding  molecules. 
Concluding,  I  believe  erroneously,  from  an  empirical  law, 
that  the  attraction  between  molecules  must  vary  inversely 
as  the  square  of  the  distance,  he  was  driven  to  the  second 
conclusion  that  if  this  were  the  case  the  cohesion  could  not 
penetrate  matter.  He  assumed,  hence,  that  the  surrounding 
molecules  absorbed,  or  neutralized,  the  lines  of  cohesive  force. 
The  direct  evidence  and  Einstein's  reasoning  leaves  little 
doubt  that  the  radius  varies  with  the  distance  apart  of  the 
molecules  and  the  only  possible  conclusion  from  this  is  that 
the  surrounding  molecules  delimit  the  field  as  Mills  supposes. 
If  it  is  a  fact  that  the  surrounding  molecules  delimit  the 
field  as  the  evidence  indicates,  cohesion  is  allied  at  once  with 
magnetism,  for  this  is  the  very  supposition  which  Ewing 
made  to  explain  some  of  the  phenomena  of  magnetism.  Each 
molecule  of  a  ferromagnetic  substance  is  supposed  to  be  a 


1  Sutherland:  Phil.  Mag.,  [6]  4,  632,  636  (1902). 

2  Mills:  Jour.  Phys.  Chem.,  15,  417  (19*  0- 


498  Albert  P.  Mathcivs 

magnet.  In  the  non-magnetic  state  the  magnetism  of  each 
molecule  is  supposed  to  be  neutralized  by  the  surrounding 
molecules,  which  have  their  magnetic  axes  variously  directed. 
The  magnetic  field  is  thus  limited  to  a  single  molecular  diam- 
eter and  will  vary  with  the  distance  apart  of  the  molecules. 
The  magnetic  field  of  each  molecule  is  delimited  by  the  sur- 
rounding molecules.  If,  however,  these  molecules  are 
oriented,  either  by  acting  on  each  ether,  or  by  external  forces, 
then  the  magnetic  fields  coincide  and  the  magnetism  may  be 
perceived  extending  outward  from  the  mass.  In  other 
wrords,  to  explain  why  magnetism  does  not  persist  in  soft  iron 
and  to  account  for  magnetic  hysteresis,  Ewing  has  made 
exactly  the  same  assumption  which  has  been  made  to  explain 
why  cohesion  does  not  extend  beyond  molecular  distances. 

It  seems  to  me  not  impossible  that  magnetism  is  the 
cohesive  attraction  of  a  molecule.  If  the  molecule  is  of  such 
a  nature,  or  shape,  that  the  total  effect  of  the  little  magnets, 
its  electron  couples,  coincide  more  or  less  completely  so  that 
the  molecule  has  a  polarity,  and  the  molecules  can  be  oriented 
in  any  way  and  held  in  position,  we  have  the  ferro  and  para- 
magnetic substances.  If  the  molecules  have  many  poles,  so 
that  there  is  no  polarity  of  the  molecules  as  a  whole,  there  is  a 
diamagnetic  substance.  The  magnetic  field  of  each  molecule 
would  be  its  cohesive  field. 

The  recent  work  of  Cotton  and  Mouton1  on  the  orienta- 
tion of  molecules  in  the  magnetic  field  seems  to  me  to  bear  out 
such  an  interpretation.  The  work  of  Weiss2  and  Langevin3 
appears  to  point  in  the  same  direction,  but  Weiss,  who  has 
considered  the  possibility  of  the  identity  of  cohesion  and 
magnetism,  states  that  he  will  shortly  show  that  they  can  not 
be  identical.  Nevertheless  it  appears  to  me  not  impossible 
that  magnetism  is  simply  a  special  case  of  cohesion,  and  if 
this  is  true  the  rotation  of  the  plane  of  polarized  light  by  op- 
tically active  substances  would  be  easily  understood. 

1  Cotton  and  Mouton:  Journal  de  Physique,  [5]  I,  40  (1911). 

2  Weiss:  Journal  de  Physique,  [5]  i,  900  (1911);  [4]  6,  661  (1907). 

3  Langevin:  Ann.  Chim.  Phys.,  5,  70  (1905). 


Relationship  between  Molecular  Cohesion  499 

Finally,  if  it  is  true  that  the  surrounding  molecules  de- 
limit the  field  of  cohesion  in  any  way  whatever,  and  that 
only  six  molecules  really  take  part  in  this  delimitation,  we  can 
derive  the  value  a/V2  of  van  der  Waals'  at  once  and  very 
simply. 

Suppose  that  each  molecule  has  a  certain  mass  of  cohes- 
ion, M,  and  that  two  molecules  attract  each  other  directly 
as  the  product  of  their  cohesive  masses  and  inversely  as  the 
fourth  power  of  the  distance  between  their  centers,  then  the 
attraction  between  two  molecules  would  be  M2K/i>4/3,  where 
D  is  the  space  at  the  disposal  of  a  single  molecule.  Since 
each  molecule  attracts  only  the  one  above,  below  and  to  each 
side,  the  pressure  per  square  centimeter  of  a  double  layer  of 
molecules  will  be  M2K/V/3  multiplied  by  the  number  of  mole- 
cules in  i  sq.  cm  or  i/V'/3,  making  M2K/V.  Since  the  at- 
traction extends  only  a  single  molecular  diameter,  we  may 
multiply  both  numerator  and  denominator  by  N2,  where  N 
is  the  number  of  molecules  in  the  volume,  V,  and  we  obtain, 
N2M2K/NV  ==  M2N2K/V2  =<*  a/V2.  M2K  has  already  been 
shown  to  be  2.98  X  io~37  (Mol.  Wt.  X  Valences)2/3. 

We  have,  as  yet,  no  proof  that  only  the  six  surrounding 
molecules  are  attracted,  although  Sutherland1  has  made  a 
similar  supposition.  But  such  may  be  the  case  nevertheless. 
Einstein,  in  his  calculation,  computed  that  each  molecule 
could  be  considered  as  lying  at  the  center  of  a  cube  and  that 
it  attracted  the  26  other  molecules  of  the  cube.  Of  course 
the  fact  that  the  value  a/V2  may  be  so  easily  derived  in  this 
way  does  not  furnish  any  proof  that  the  attraction  is  inversely 
as  the  fourth  power  of  the  distance.  But  I  know  of  no  other 
derivation  of  a/V2  which  involves  so  few,  or  less  radical, 
assumptions. 

The  general  conclusion  of  the  paper  is  then,  that  cohesion, 

1  Sutherland:  Phil.  Mag.,  [6]  17,  667  (1909).  "The  total  potential 
energy  of  a  number  of  like  molecules  is  the  same  as  if  each  caused  its  own  domain 
to  be  uniformly  electrized  with  an  electric  moment  proportional  to  the  linear 
dimensions  of  the  domain,  the  direction  of  electrization  being  such  that  in  general 
any  molecule  attracts  its  six  immediate  neighbors." 


500  Albert  P.  Mathews 

being  a  function  of  molecular  weight  and  valence,  is  a  function 
of  the  number  of  electron  couples  of  the  valences  and  atoms, 
and  is,  hence,  probably  of  a  magnetic  nature.  Magnetic 
substances  may  be  supposed  to  be  substances  in  which,  owing 
to  the  orientation  of  the  molecules,  or  to  their  polarity,  or 
both  these  causes,  the  cohesive  fields  of  the  molecules  are  not 
delimited  or  neutralized  by  the  surrounding  molecules  so  that 
the  cohesional  attraction  becomes  apparent  at  more  than 
molecular  distances,  and  under  such  circumstances  the  sub- 
stance is  said  to  be  magnetic. 

University  of  Chicago 


THE  INTERNAL  PRESSURES  OF  UQUIDS 


BY  ALBERT  p.  MATHEWS 

The  fundamental  significance  of  the  constant  "a"  of  van 
der  Waals'  equation  makes  its  exact  determination  important. 

Various  methods  have  been  proposed  for  the  determination 
of  this  constant,  but  none  of  them  are  entirely  satisfactory. 
In  a  recent  paper1  attention  was  drawn  to  a  method  by  which 
it  could  be  determined  from  the  surface  tension  by  the  use  of 
Thomas  Young's  formula,  T  =  rK/3,  combined  with  the 
law  of  Ramsay  and  Shields,  and  the  values  thus  computed 
were  shown  to  be  closely  similar  for  most  substances  to  the 
values  computed  by  van  der  Waals'  method  from  the  critical 
temperature  and  pressure,  but  in  some  cases  they  deviated 
considerably  from  his  values.  I  found,  also,  that  the  values 
of  the  constant  "a"  obtained  by  this  method  were  simple 
functions  of  the  products  of  the  molecular  weight  and  the 
number  of  valences  in  the  molecule  and  that  they  could  be 
computed  from  these  values.  Inasmuch  as  the  method 
used  in  computing  "a"  from  the  surface  tension  involved 
the  value  of  the  density  at  absolute  zero,  which  was  computed 
from  Cailletet  and  Mathias'  law  of  the  rectilinear  diameter, 
and  involved,  therefore,  some  uncertainty  and  was  certainly 
too  high,  it  was  desirable  to  find  a  method  of  computing  "a" 
directly  from  the  surface-tension  measurements. 

The  desire  of  finding  such  a  method  was  stimulated  by  the 
present  great  uncertainty  of  the  value  of  the  internal  pressures 
of  liquids.  Traube2  has  within  the  past  few  years  computed 
the  internal  pressure  for  many  liquids,  but  the  results  he  has 
obtained  are,  in  my  opinion,  unreliable  because  his  method  of 
computation  involves  the  use  of  the  value  "&"  the  real  molec- 
ular volume  or  co-volume,  a  very  doubtful  value.  The  values 
he  finds  for  the  internal  pressure  at  zero  degrees  are,  also, 
widely  different  from  those  computed  by  the  use  of  ' V  found 


1  Mathews:  Jour.  Phys.  Chem.,  17,  154  (1913). 

2  Traube:  Zeit.  phys.  Chem.,  68,  291  (1909). 


604  Albert  P.  Mathews 

at  the  critical  temperature;  and  in  some  cases  they  are  not 
more  than  half  those  calculated  recently  by  Lewis1  from  the 
latent  heats  of  expansion  of  liquids. 

Walden,2  also,  has  recently  calculated  the  value  of  "a"  and 
the  internal  pressure  from  the  surface  tension.  His  calculation 
is,  however,  almost  wholly  empirical. 

It  is  based,  first,  on  Stefan's  conclusion3  that  it  takes  one- 
half  the  work  to  move  a  particle  into  the  surface  which  is 
required  to  carry  it  all  the  way  to  the  vapor;  and,  second, 
upon  an  empirical  relationship  found  by  Walden  between  the 
surface  tension  and  the  molecular  latent  heat  at  the  boiling 
point.  It  is,  however,  by  no  means  certain  that  Stefan's 
conclusions  are  correct  and  his  reasoning  does  not  carry  con- 
viction. There  is,  also,  probably  an  error  in  the  assumption 
that  the  molecules  do  not  change  in  size  on  passing  from  the 
liquid  to  the  vapor  and  that  the  latent  heat  of  vaporization 
represents  only  the  work  done  in  overcoming  molecular  co- 
hesion. Finally  Walden's  values  for  "a"  resemble  Traube's. 
"a"  is  always  much  less  than  when  computed  by  van  der 
Waals'  method  from  the  critical  data  and  much  less  than  the 
values  of  Lewis.  The  values  which  Walden  has  obtained  are 
about  two-thirds  the  values  given  in  this  paper. 

Values  still  smaller  have  been  computed  by  Davies4  from 
the  latent  heat  of  vaporization.  The  values  he  obtains  are 
only  about  one- third  those  of  Lewis.  Winther5  has  still  other 
results. 

Many  modifications  of  van  der  Waals'  equation  have  been 
proposed  in  which  "a"  was  considered  variable  with  the  tem- 
perature and  "6"  more,  or  less,  constant.  These  attempts 
have  not  been  fruitful.  It  is  far  more  probable  that  "6," 
the  volume  correction,  varies  with  temperature  and  volume 
and  that  "a,"  which  is  the  ''mass"  factor  of  the  cohesion,  is 


1  Lewis:  Phil.  Mag.,  [6]  25,  61  (1912). 

2  Walden:  Zeit.  phys.  Chem.,  66,  385  (1909). 

3  Stefan:  Wied.  Ann.,  29,  655  (1886). 

4  Davies:  Phil.  Mag.,  [6]  24,  422  (1912). 

5  Winther:  Zeit.  phys.  Chem.,  60,  603  (1907). 


The  Internal  Pressures  of  Liquids 


605 


constant,  "a,"  indeed,  as  van  der  Waal's  has  repeatedly 
shown,  should  be  considered  constant  unless  association,  or 
quasi-association,  occurs,  "a"  contains  the  factor  N2,  N 
being  the  number  of  molecules  in  the  volume,  V,  hence  any 
association  will  lower  "a"  by  this  factor. 

The  wide  divergence  of  these  various  values  proposed  for 
the  internal  pressure  is  shown  in  Table  i  expressing  the  internal 
pressure  in  atmospheres  at  zero  degrees,  except  in  the  case  of 
Walden  where  the  values  are  for  the  boiling  points  and  Davies 
fori50C. 

i 


Substance 

Davies 

15° 

Traube 

0° 

Walden 
b.  p. 

v.  d.  Waals 

0° 

Lewis 

0° 

Winther 

Benzene 

I  102 

1380 

1570 

2494 

2639 

1792 

Toluene 

1188 

1180 

1340               2228 

2847 

— 

Cymene 

661 

— 

—                   — 

2718 

— 

Ether 

778.9 

990 

|l2IO(                I723 

1932 

I22O 

CC14 

1076 

1305 

1490                 2205 

2518 

1680 

CS2 

1683 

1980 

2170                 3363 

2917 



Et  acetate 

— 

22IO 

^1280^ 
(1340) 

2466 

I486 

In  this  paper  are  given  the  values  of  "a"  obtained  in  several 
quite  different  ways,  all  of  which  yield  closely  agreeing  results. 

1.  The  first   method   is   a   computation   from   the  surface 
tension.     The  assumption  involved  in  this  method  is  the  depth 
of  the   surface  film  expressed  in  the  number  of  molecular 
layers.     That  the  assumption  is  correct  is  proved  by  the  out- 
come. 

2.  The  second  method  is  a  modification  of  Thomas  Young's 
method  combined  with  the  law  of  Eotvos  as  developed  in  my 
former  paper,  but  with  certain  corrections. 

3.  In   the   third   method   "a"   is  computed  from  van  der 
Waals'  equation  at  the  critical  temperature,  the  assumption 
being  made  that  in  all  normal  substances  bc  -•  =  2V 0  ==  2VC/S, 
S  being  the  critical  coefficient  and  equal  to  RTC/VCPC. 

4.  In  the  fourth  method  "a"  is  computed  from  the  internal 


606  Albert  P.  Mathews 

latent  heat  of  vaporization  close  to  the  critical  temperature. 
The  only  assumption  made  here  is  that  Mills'  or  Dieterici's 
formula  for  the  internal  latent  heat  is  more  correct  close  to 
the  critical  temperature  than  the  internal  latent  heat  computed 
by  Biot's  formula. 

5.  Finally  "a"  is  computed  from  the  number  of  valences 
and  the  molecular  weight  by  the  formula:  a  =  C(M  X  Val)2/3. 

1.  Computation  of  "a"  from  the  Surface  Tension 

The  surface  film  is  determined  by  the  difference  of  cohesive 
attraction  in  the  vapor  and  liquid.  The  surface  energy  must, 
hence,  be  a  function  of  the  difference  in  cohesive  energy  in  the 
liquid  and  vapor,  or  of  the  expression  a(i/V/ —  i/VJ.  This 
cohesive  energy  has  been  lost  in  passing  the  liquid  through 
the  surface  layer  which  separates  the  two  states  and  should 
be  calculable  from  the  surface  tension. 

Suppose  we  have  a  sphere  of  a  gram  mol  of  a  liquid  in  con- 
tact at  all  points  with  its  saturated  vapor.  Its  density  is 
uniform  except  in  the  surface  film  where  it  decreases  by  a 
series  of  steps  from  liquid  to  vapor  density.  The  surface 
film  may  be  conceived  as  a  series  of  concentric  shells,  each  a 
molecular  diameter  thick,  and  each  outer  one  less  dense  than 
the  inner  until  the  state  of  uniform  vapor  density  is  reached. 
Furthermore,  on  passing  from  one  of  these  molecular  shells 
lying  within  to  the  one  next  beyond  it,  always  the  same  amount 
of  cohesive  energy  will  be  lost,  if  the  density  diminishes  uni- 
formly from  shell  to  shell. 

The  surface  tension  T,  is  the  tension  along  a  line  i  cm.  in 
length  in  the  surface  film  and  one  molecular  layer  deep.  It 
represents  the  force  necessary  to  stretch  the  surface,  that  is 
to  rupture  one  of  these  shells,  and  thus  drag  one,  or  more, 
molecules  from  the  inner  core  of  uniform  density  into  the  first 
concentric  shell;  and  of  course  the  force  necessary  to  drag 
molecules  from  the  first  shell  to  the  second,  and  from  the  second 
to  the  third  and  so  on,  since  the  same  force  is  necessary  to 
drag  molecules  from  each  inner  shell  to  the  next  outer.  This 
tension,  T,  is  numerically  equal,  also,  to  the  surface  tension 


The  Internal  Pressures  of  Liquids  607 

/ 

energy  per  square  cm.  of  the  surface  film.  For  each  con- 
centric shell  of  the  surface  one  molecular  diameter  deep,  the 
surface  energy  is,  then,  T  times  the  surface,  or  TV*73;  and  the 
total  energy  in  the  surface  or  a,  will  be  equal  to  this  amount 
multiplied  by  the  number  of  shells,  which  we  shall  represent 
by  the  letter  n,  thus  we  have  the  equation : 

(1)  a  =  TVl/3n 

If  now  a  gram  mol  of  liquid  passes  from  liquid  to  vapor  it 
must  pass  through  this  surface  in  which  surface  energy  is 
gained  at  the  expense  of  the  cohesive  energy  which  is  lost. 
To  determine  the  total  amount  of  energy  which  is  thus  changed 
in  passing  the  whole  gram  mol  through  the  surface,  it  is  only 
necessary  to  determine  how  many  times  we  shall  have  to  make 
a  new  surface  shell  until  the  whole  of  the  gram  mol  has  passed 
through.  Since  the  total  number  of  molecules  in  the  gram 
mol  is  N,  and  there  are  in  a  surface  shell  N2/3  molecules,  we 
shall  have  to  make  a  new  surface  N/N2/3  times,  or  N1/3  times. 
The  total  energy  then  which  will  be  gained  as  surface  tension 
energy  will  be  S,  or 

(2)  S  =  TVY*NY*n. 

This  same  value  may  be  obtained,  also,  in  the  following 
way:  The  surface  tension  measures  the  force  necessary  to 
overcome  the  surface  tension  pressure  along  a  line  i  cm  long 
and  a  molecular  diameter  deep.  The  surface-tension  pressure 
per  sq.  cm  acting  in  the  plane  of  the  surface  is  hence  T/v1/3, 
i)  being  the  volume  of  a  single  molecule.  Multiplying  numera- 
tor and  denominator  by  N1/3  we  have  the  pressure  per  square 
cm  N1/3T1/3/V;/3.  If  this  pressure  work  through  the  volume  Vt, 
the  volume  of  one  gram  mol,  we  have  the  surface  tension  energy 
if  a  whole  gram  mol  were  present  as  a  surface  shell,  or  N1/3TV*/3. 
Multiplying  this  by  the  number  of  shells,  or  n,  we  have  our 
former  expression. 

Equation  (2)  contains  the  unknown  factor  "n,"  that  is  the 
number  of  layers  one  molecular  diameter  thick  constituting 
the  surface  film.  Since  I  knew  of  no  way  of  measuring  this, 


6o8  Albert  P.  Mathews 

the  following  assumption  was  made  based  on  van  der  Waals' 
conclusion  that  the  surface  film  is  infinitely  thick  at  the  critical 
temperature.  At  absolute  zero,  where  the  molecules  are 
presumably  in  contact,  it  may  be  assumed  that  the  surface 
film  is  only  a  single  molecular  diameter  deep.  At  the  critical 
temperature,  on  the  other  hand,  it  must  be  infinitely  deep. 
That  is,  no  matter  how  many  layers  of  molecules  one  passes 
over,  one  can  never,  at  that  temperature,  get  to  a  region  of 
differing  density.  Between  absolute  zero  and  the  critical 
temperature  the  depth  of  the  surface  film  must  lie  between 
these  two  values,  increasing  with  the  temperature,  and  pre- 
sumably in  all  normal  substances  at  corresponding  tempera- 
tures it  will  be  the  same  number  of  molecular  layers  thick. 
I  accordingly  made  the  guess  that  it  would  be  equal  to 
(TC/(TC  —  T))2/3  molecular  diameters  since  this  fraction  is  equal 
to  (d0/(di — dj)2  (see  page  617).  This  guess  turned  out  to  be 
correct  if  Eotvos  surface-tension  figures  are  used,  but  if  Ram- 
say and  Shields'  are  taken  the  fraction  must  be  raised  to  the 
0.76  power  and  even  then  the  value  of  "a"  computed  by  this 
assumption  runs  down  near  the  critical  temperature.  Since 
Eotvos  measured  the  surface  tension  by  a  method  which  en- 
tirely avoided  any  assumption  as  to  the  angle  of  contact  and 
Ramsay  and  Shields  used  the  capillary  method,  which  involves 
such  an  assumption,  I  believe  Eotvos  figures  and  his  statement 
of  the  law  is  to  be  preferred.  That  his  formula  of  TV*/3  =  2.27 
(Tc  —  T)  is  to  be  preferred  on  other  accounts  is  shown  by  the 
calculations  which  follow: 

The  total  surface  energy  gained  by  passing  a  gram  mol 
through  the  surface  is  hence : 

(3)  S  -  TV'/3N1/3(TC/  (Tc  —  T)) o.76  ergs ;  or 

(4)  2  -  TV;/3N1/3(TC/  (Tc  —  T))2/3  ergs. 

Formula  (4)  is  to  be  preferred,  when  the  surface  tension  is 
measured  by  methods  which  do  not  involve  the  angle  of 
contact. 

We  only  have  left  to  find  the  relation  between  the  amount 
of  energy  thus  lost  and  the  difference  in  the  cohesive  energy 


The  Internal  Pressures  of  Liquids  609 

in  a  gram  mol  of  liquid  and  vapor,  respectively.  I  think  that 
the  total  surface-tension  energy  must  be  one- third  of  the  total 
difference  in  cohesive  energies  in  equal  weights  of  the  two  phases 
separated  by  the  surface.  The  energy  in  the  surface  is  an 
expression  of  the  difference  in  cohesive  pressure  in  one  direction 
only,  whereas  the  two  phases  differ  in  their  cohesion  in  three 
dimensions.  That  the  value  one- third  is  correct  is  shown  by 
the  computations  which  follow.  The  value  one-third  was  that 
adopted  also  by  Young  more  than  a  century  ago,  but  his 
reasoning  is  so  condensed  that  it  is  hard  to  follow.  His 
statement  is  as  follows  i1 

"Upon  these  grounds  we  may  proceed  to  determine  the 
actual  magnitude  of  the  contractile  force  derived  from  a  given 
cohesion  extending  to  a  given  distance.  Supposing  the  cor- 
puscular attraction  equable  throughout  the  whole  sphere  of 
its  action,  the  aggregate  cohesion  of  the  successive  parts  of 
the  stratum  will  be  represented  by  the  ordinates  of  a  parabolic 
curve;  for  at  any  distance  x  from  the  surface,  the  whole  in- 
interval  being  a,  the  fluxion  of  the  force  will  be  as  dx(a  —  x), 
since  a  number  of  particles  proportional  to  dx  will  be  drawn 
downwards  by  a  number  proportional  to  a,  and  upwards  by 
a  number  proportional  to  x,  and  the  whole  cohesion  at  the 
given  point  will  be  expressed  by  ax  —  *2/2;  and  this  at  last 
becomes  a2/2,  which  must  be  equal  to  the  undiminished  co- 
hesion in  the  direction  of  the  surface.  Consequently  the  dif- 
ference of  the  forces  acting  on  the  sides  of  the  elementary 
cube  will  everywhere  be  as  a2/2  —  ax  +  x2/2  and  the  fluxion 
of  the  whole  contractile  force  will  be  dx(a2/2 — ax  +  *2/2)> 
the  fluent  of  which  when  x  ==  a  becomes  a3/6,  which  is  V3  of 
a  xa*/2,  the  whole  undiminished  cohesion  of  the  stratum." 
"We  may,  therefore,  conclude,  in  general,  that  the  contractile 
force  is  one- third  of  the  whole  cohesive  force  of  a  stratum  of 
particles  equal  in  thickness  to  the  interval  to  which  the  primi- 
tive equable  cohesion  extends,"  or  T  =  aK/3. 

Accepting  this  coefficient  of  1/3  of  Young  in  place  of  that  of 


1  Young,  T:  "Article  on  Cohesion,"  collected  works,  p.  460. 


6 io  Albert  P.  Mathews 

Y,  of  Stefan,   or  3/20  as  computed  by  Lord  Rayleigh,  we  have 
the  complete  formula 

(5)  0(i  /V,  -  i / V.)  1 3  --  TV:/3NI/3(Tc/ (T,  —  T))v>. 
Changing  to  density  in  place  of  volume  on  the  left  hand  side 

we  have 

(6)  a  -  3rv;/3N1/3M(Tc/ (Tc—  T))2/3/ (^  —  ^) ; 

or  if  Ramsay  and  Shields'  surface-tension  figures  are    used 

(7)  a  =  3^/3N1/3M(Tc/  (Tc  —  T))°-*V  (^  _  </„) . 

The  result  is  given  in  dynes  for  gram  mol  quantities.     M  is 
the  molecular  weight;  d1  and  dv,  liquid  and  vapor  density, 
respectively;  N,  the  number  of  molecules  in  a  gram  mol,  is 
6.21   X  io23;  T  is  the  surface  tension  in  dynes;  Vj,  the  volume  / 
of  a  gram  mol  at  temperature,  T. 

From  the  foregoing  it  appears  that  1/s  of  the  internal  latent 
heat  of  vaporization  is  due  to  the  cooling  caused  by  the  in- 
crease of  the  surface  brought  about  by  the  transfer,  of  molecules 
from  the  region  of  uniform  density  into  the  surface,  and  their 
passage  through  the  surface. 

In  Table  2,  I  have  given  the  calculation  of  "a"  by  formula 
(7)  for  a  number  of  substances  using  Ramsay  and  Shields', 
or  Ramsay  and  Acton's  or  Renard  and  Guye's  surface-tension 
determinations  and  the  densities  from  S.  Young's1  recent 
work. 

In  Table  2  the  constancy  of  "a"  is  shown  to  be  good  for 
normal  substances,  except  near  the  critical  temperature  where 
it  generally  falls  off  somewhat.  This  may  be  due  to  the 
inaccuracy  of  the  surface  tension  close  to  the  critical  tempera- 
ture, but  it  is  more  probably  due  to  the  fact  that  the  thickness 
of  the  surface  layer  in  molecular  diameters  is  not  properly 
represented  by  the  expression  (TC/(TC — T))°'76  and  possibly 
to  the  influence  of  the  angle  of  contact. 

There  is  in  general  a  tendency  of  the  value  of  "a"  to  rise 
except  near  the  critical  point,  and  this  tendency  is  most  pro- 
nounced in  an  associating  substance  such  as  ethyl  alcohol. 

The  agreement  is  admirabj^clear  to  the  critical  temperature 

1  Young,  S:  Proc.  Roy.  Dublin  Soc.,  12,  374  (1910). 


The  Internal  Pressures  of  Liquids 


611 


if  the  computation  is  made  by  Eotvos  formula,  for  TV*/3  in 
the  manner  shown  farther  on  (Table  6). 

I  may  repeat,  to  make  the  point  quite  clear,  that  I  think  by 
taking  the  value  (TC/(TC— T))°-76  in  place  of  the  theoretical 
value  (TC/(TC — T))2/3  for  these  surface-tension  measurements 
we  offset,  at  least  approximately,  some  constant  source  of 
error,  possibly  the  angle  of  contact,  involved  in  the  determination 
of  the  surface  tension  by  the  capillary  method.  The  opinion 
has  been  expressed  by  others  that  the  error  due  to  the  neglect 
of  the  angle  of  contact,  or  the  assumption  that  it  is  zero,  will 
increase  with  the  temperature. 

TABLE  2 

"a"  in  dynes  for  a  gram  mol  computed  by  formula  (7) 
Methyl  formate          Ethyl  acetate  Benzene 


t° 

a  X  icr13 

t° 

a  X  icr13 

t° 

a  X  iQ-  13 

20 

.-217 

+  20 

2.338 

II  .2 

2  .214 

40 

.224 

80 

2.366 

46 

2  .220 

60 

.228 

IOO 

2.366 

80 

2.22O 

80 

•233 

120 

2.370 

I2O 

2.235 

100 

•237 

I4O 

2.367 

1  60 

2  .242 

120 

1.237 

1  60 

2.368 

200 

2.242 

140 

1.231 

1  80 

2.368 

240 

2.225 

1  60 

I  .218 

2OO 

2-353 

260 

2.179 

1  80 

I-I93 

220 

2-355 

270 

2.081 

200 

1.058 

240 

2.193 

280 

I.52I 

2IO 

0.885 

245 

2  .  107 

288.5 

Tc 

214 

Tc 

250.1 

Tc 



-  — 

Chlorbenzene 


Carbon  tetrachloride 


Ether 


9-5 

2  .  944       i  i  .  8 

2-393 

—89.2 

2.038 

45-6 

2.947 

46 

2.404 

+  20 

2.044 

77.1 

2  .962 

80 

2.387 

40 

2.039 

150 

2.958 

120 

2.405 

60 

2  .072 

1  80 

2.965 

I4O 

2.4II 

70 

2.023 

200 

2-975 

1  60 

2.422 

80 

2  .021 

220 

2.977 

200 

2.431 

IOO 

2.025 

260 

2.984 

22O 

2  .401 

no 

2.023 

310 

2-977 

240 

2-344 

120 

2.020 

359-2 

TC 

260 

2.187 

I4O 

1.990 



270 

2-483 

1  6O 

I.9I8 



-  — 

283 

Tc 

193 

2-745 





-  — 

193.8 

Tc 

612 


Albert  P.  Mathews 


Methyl  butyrate 


TABLE  2 — (Continued} 
Cymene  Anisol 


Toluene 


-    t 

a  X  io~13 

* 

a  X  io-13          t 

a  X  io-13 

t 

a  X  io-13 

10 

46.2 

78.2 

IOO 
T  7  •?     £ 

2  .706 

2.964 

3-005 

3.040 

11.9 
31-7 
74-5 
108.9 

4.982          II  .  I 

5-013  !     33-5 
5.026        88 

5-055  ||  119 

3-424 
3-452 
3-471 
3.486 
i    /in8 

I3-I 
29.1 

78.2 
!   132.5 

2.744 
2.788 
2.827 
2.860 

L62  •  5 

TQc 

.   1  1VJ 

M4-9 

•°75       H7-9 

3  -49° 

105 

•°73 

103.4 

•  T43 

o^Q 

.049 

i; 

230 

oSr     i 

•093 
T. 

I 

Piperidine 


CS, 


CHCL 


Methyl  acetate 


15.2 
46.6 
78.4 

2.638 

2  .664 
2  .672 

9-7 
46 
61 

1.277 

I  .222 

1-434 

10.2 

45-5 
77-6 

1.837 
1.860 
1.874 

io     1-719 
46.2  i  1.727 
78.3   1.746 

J32  -5 

•  791 

J32  -4   r  -777 

185     1-77° 

200     i  .  740 

215     1.720 

ooo  n       T- 

Kthylene 
dibromide 


Methyl 
isobutyrate 


Ethyl  alcohol     Ethyl  propionate 


12  .2 

44-9 

77-2 

2.776 
2.842 

2  -912 

3-074 

46.2 

78.2 

IOO 

2.871  i 
2.894 

2  .920 
2.932 

20    j  0.951 

40    o  .  966 
loo    1.055 

150   1.157 

10 

46.2 

78.2 

IOO 

2.903 
2.932 
2.969 

3-004 
_  ^s-  T 





132  .2 
I85 

2-937 
2.941 

180    1.235 

220      1.485 

132.2 

185 

3.061 
3-047 





237.6 

i  267.7 

•947 

2-913  ! 

Tc 

i   

2  IO 
237.6 
272.9 

.OOO 
3.010 

Tc 

Propyl  acetate  Methyl  propionate 

Propyl  formate     Ethyl  iodide 

IO 

46.2 

78.2 

IOO 

132.6 

185 

210 
238.2 
276.2 

2.917 

2-954 
2.966 
2.981 

3-010 
3.011 
2.999 

2  .980 

Tc 

10 

46.2 

78.2 

132.6 
184.9 

237-7 
250 

257-4 

2.287  1 
2.302 

2.329 
2.350  II 

2.365- 

2.278 

I  .962    !j 

Tc 

IO 

46.2 

78.2 
85 
131-7 

2IO 

237 
264.85 

2.270 

2.278 
2.331 

2-334 
2-356 
2-348 

2-339 
2.312 
Tc 

19.1 

78.2 
|  281 

2.034 
2.044 

lc 

Metaxylene 
io           3-408 



The  Internal  Pressures  of  Liquids  613 

2.  Derivation  of  "a"  from  the  Surface  Tension  by  Eotvos 

Law 

By  the  law  of  Eotvos  the  surface-tension  energy  TV*/3  is 
equal  to  C(TC — T).  The  surface-tension  energy  is  a  linear 
function  of  the  temperature  counting  downward  from  the 
critical  temperature.  The  derivation  of  TV*/3  and  N1/3TV2/3 
has  already  been  given  on  page  607. 

a.  What  is  C  of  Eotvos? 

Eotvos  found  that  C  varied  between  2.27  and  2.34  as  is 
shown  in  Table  4,  but  he  believed  the  variation  to  be  acci- 
dental and  that  C  should  be  constant  for  all  substances.  It 
has  since  been  shown  that  C  is  not  constant.  What  C  is  may 
be  shown  as  follows : 

Since  the  surface  energy  decreases  uniformly  with  an  in- 
crease of  the  kinetic  energy  of  the  molecules,  and  is  accordingly 
a  linear  function  of  the  temperature,  one  of  the  constitutents 
of  C  must  be  the  gas  constant  R;  and  since  there  are  onlyN2/3 
molecules  in  the  surface,  where  N  is  the  number  in  a  gram  mol, 
R  must  be  R  for  a  gram  mol  divided  by  N1/3.  The  remainder 
of  C  should  be  1/3  the  ratio  of  the  internal  to  the  external  pres- 
sure at  the  critical  temperature  as  that  is  the  point  of  depart- 
ure. Young  has  shown  that  the  surface-tension  pressure  is  1/3 
the  cohesive  pressure;  and  the  greater  the  external  pressure 
the  less  important  the  internal  pressure  will  be.  Hence  C,  I 
thought,  must  equal  KCR/3PCN1/3.  While  the  foregoing  rea- 
soning was  not  entirely  convincing  the  result  turned  out  to 
be  correct,  I  believe,  as  will  presently  be  shown.  I  have 
uniformly  taken  N  as  6.21  X  io23  and  R  as  8.321  X  io7. 

(8)  TVl/s  =  KcR(Tc  —  T)  /3PcN1/3. 
Since  Kc  ==  a/V*  we  have 

(9)  TVl/3  =  aR(Tc  —  T)  /3V'PCN1/3 
(io)                   a  =  3TcVcN1/3rv;/3/  (Tc  —  T)S, 

since  RTC/VCPC  =  S,  and  R  ==  SVCPC/TC. 

Formula  (io)  gives  the  second  method  of  computing  "a." 


614 


Albert  P.  Mathews 


The  following  values  in  Table  3  were  computed  by  formula 
(10)  from  Schiff's  surface-tension  figures  at  the  boiling  point. 
a  is  in  dynes  per  gram  mol. 

TABLE  3 


Substance 

s 

a  X  io-12 

Methyl  acetate 

3-940 

15.90 

Propyl  acetate 

3-933 

28.14 

Diisobutyl 

3.811 

40.01 

Benzene 

3-754 

20.52 

Ether 

3.810 

IQ.  12 

Hexane 

3-831 

27.22 

CC14 

3.676 

22  .60 

These  results  are  uniformly  somewhat  lower  than  those 
computed  from  Ramsay  and  Shields'  figures  by  formula  (7). 

Returning  to  the  value  C  of  Eotvos  formula,  the  following 
computation  shows  that  it  has  in  it  the  components  ascribed 
to  it. 

It  was  believed,  for  the  reasons  given,  that  C  of  Eotvos  must 
be  equal  to  KCR/3PCN1/3.  The  ratio  of  the  internal  to  the  ex- 
ternal pressure  is  supposed  to  be,  at  the  critical  temperature, 
very  approximately  equal  to  7.  Its  real  value  is  as  follows: 
If  we  assume  that  bc  of  van  der  Waals'  equation  is  always 
twice  the  volume  at  absolute  zero,  then  bc  =  2V0.  Since 
V0  -  VC/S,  bc  ==  2VC/S.  If  this  is  so  then  the  ratio  between 
Kc  and  Pc  is  equal  to  (S2  — S*  +  2)/(S  — 2).  S  =-  RTC/VCPC. 
Hence  C  of  Eotvos  must  be  as  follows : 

(i  i)  C  =  (S2  —  S  +  2)R/(S  —  2)3N1/a. 

Formula  (n)  can  now  be  tested  since  C  is  known  to  lie 
between  2.27  and  2.34  for  several  non-associating  substances. 
The  results  of  a  computation  of  C  by  this  formula  and  the 
values  given  by  Eotvos  are  compared  in  Table  4. 

The  results  are  evidently  closely  similar,  but  unfortunately 
Eotvos  did  not  give  the  value  of  C  for  many  substances  of 
which  S  is  known. 


The  Internal  Pressures  of  Liquids 
TABLE  4 


615 


Substance 

S 

C 
computed 

C  found  by  Eotvos 

Methyl  acetate 
Methyl  butyrate 
Ethyl  alcohol 
Pentane  (n) 
Ether 
Benzene 
Oxygen 
Carbon  dioxide 
Propyl  acetate 
Carbon  bisulfide 
Chloroform 
Ethylene  bromide 

3-943 
3-907 
4.025 
3.761 
3.806 

3-794 
3-40 
3-44 
3-933 

2.273 
2.275 

2  .270 
2.285 
2.280 
2.279 
2-355 
2-344 
2.280 



2.280  (6-62°);   2.26  (62-120°) 

2  .280 

2-37 
2.30 

2.27 





2.  The  Computation  of  "a"  from  Thomas  Young's  Formula 

As  pointed  out  in  an  earlier  paper,  the  first  method  pro- 
posed for  computing  the  internal  pressure  was  Young's, 
namely : 

(12)  T  =  rK/3  =  m/V23 

r  being  the  radius  of  action.     If  r  is  taken  at  absolute  zero 
as  equal  to  i//3  we  have  finally 


(13) 


Tv/3  = 


M2K  is  the  factor  "a"  for  a  single  molecule  and  v0  the  volume 
of  a  single  molecule  at  absolute  zero.  In  my  former  paper 
DO  was  assumed  for  all  except  the  simple  gases  to  be  vc/4,  and 
for  those  gases  it  was  taken  as  vc/3.6.  Timmermans1  has 
recently  confirmed  S.  Young's  finding  that  the  rectilinear 
diameter  law  gives  too  high  values  for  the  density  at  low 
temperatures  and  that  van  der  Waals  is  correct  in  taking  the 
density  at  absolute  zero  as  S  times  the  critical  density,  where 
S  is  the  critical  coefficient,  or  RTC/VCPC,  which  varies  with 
different  substances  between  3.4  and  4.  Tv20/3  I  formerly 
computed  by  Ramsay  and  Shields'  equation  assuming  that  it 


Timmermans:  Proc.  Roy.  Dublin  Soc.,  [N  S]  13,  310  (1912). 


6i6  Albert  P.  Mathews 


held  at  low  temperatures  and  that  T^/3  was  equal  to  2.19- 
(Tc  —  6)/N2/3  dynes.  This,  however,  gives  values  uniformly 
lower  than  method  i  and  I  have  accordingly  reverted  to  Eotvos 
original  formula  as  already  stated  according  to  which 

(14)  TV2/3  =  C(TC  —  T). 

The  theoretical  surface-tension  energy  at  absolute  zero 
should  be,  then,  CTC  ergs  for  a  gram  mol,  or  CTC/N2/3  ergs  for 
a  single  molecule.  Substituting  in  (13)  we  have 

(15)  M2KS/3^C  =  CTC/N2/3. 

Changing  to  the  total  volume  V,  in  place  of  the  volume  of  a 
single  molecule,  we  have  : 

(16)  a  =  N2M2K  =3CN1/3VcTc/S. 

Since  S  =  RTC/PCVC  by  substitution  in  the  foregoing  we 
have: 

(17)  '       a  =3CNV3PCV*/R  ergs. 

The  value  of  C  has  been  given  in  (i  i).  It  can  be  found  also 
by  comparing  (17)  with  (29)  which  follows.  Substituting 
its  value  we  have  : 

(18)  a  =  (S2  —  S  +  2)PcVc/(S  —  2) 

which  is  identical  with  the  formula  derived  from  van  der 
Waals'  equation  on  the  basis  that  bc  =  2VC/S.  Young's 
formula,  then,  at  absolute  zero  yields  the  same  result  as  the 
others  when  combined  with  Eotvos,  if,  however,  we  make 
no  assumption  as  to  C,  but  take  it,  as  Eotvos  thought  it  should 
be  as  constant  for  all  substances,  we  obtain  the  approximately 
correct  value  of  "a"  for  all  except  very  simple  substances: 

(19)  a  =  3  X  2.27NV3VcTc/S. 

Computations  of  "a"  by  formula  18  and  19  are  given  in  Table  9. 
We  may  check  the  foregoing  reasoning  in  the  following  way 
avoiding  any  assumption  of  what  fraction  of  Vc  bc  is.  Taking 
Young's  formula:  T  ^=  rK/3,  r  being  equal  to  vl/3  at  absolute 
zero,  multiplying  both  sides  by  v2o/3  and  then  by  N  we  have  : 


The  Internal  Pressures  of  Liquids 


617 


(20)  N3TV3  =  VoKo/3. 

Dividing  by  Tc  and  remembering  that  by  (8) 


(21)  K0Vo/3Tc  =  KcR/3Pc. 

As  K0  -=  a/Vl,  and  Kc  =  a/V'  and  V0  ••  VC/S 

(22)  i/VoTc  =  R/V^Pc. 
Therefore 

(23)  S  -  RTc/PcVc. 

Formula  23  is  true. 

We  may  also  check  our  reasoning  as  follows  :  From  for- 
mula (6)  a  =  3MN1/3TV^/3(TC/(TC—  T))2^/^—  <y  and  from  (8) 
3N^TV'/3  «  KCR(TC  —  T)/PC  we  have 

(24)  a  «  KcRM(Tc  —  T 
hence 

(25)  ^  —  </„  .  RM(TC  — 

The  values  of  Jj  —  -dv  computed  by  (25)  for  ethyl  acetate 
compare  as  shown  in  Table  5  with  those  found  by  S.  Young. 

TABLE  5  —  ETHYL  ACETATE,  d^  —  do 


t 

Computed 

Found  by  S.  Young 

-83.4° 

1.078 

I  .022 

(Timmermans) 

o 

o  .  9490 

0.9244 

1  60 

0.8007 

0.7910 

200 

0-5555 

0.5630 

240 

0.3356 

0.3279 

249 

0.2071 

O.I55I 

249-1  (Tc) 

0.0000 

0.0000 

At   absolute    zero     (25)    becomes   d0  ==  RMTC/V'PC  =  Sdc 
which  is  correct. 

Substituting  this  value  in  (25)  we  have 
(26)  d,  —  dv=  </0((Te  —  T)  /Tc)  v.. 

d0  computed  by  (26)  for  normal  pentane  using  Timmerman's 
data  for  densities  below  zero  and  S.  Young's  above  is  as  follows : 


6i8 


Albert  P.  Mathews 


/ 

do 

t 

do 

—136.5 

0.8611 

—35-3 

0.8580 

—123.3 

0.8581 

—13.1 

0.8641 

II6.2 

0.8578 

—    6.2 

0.8603 

—  in  .6 

0.8576 

0 

o  .  8603 

—104.85 

0.8570 

40 

0.8685 

—  74-25 

0.8556 

80 

0.8776 

—  73-95 

0.8570 

IOO 

0.8818 

—  63.3 

0.8571 

140 

0.8882 

—  53-6 

0.8566 

1  80 

0.8832 

—  45-0 

0.8571 

190 

0.8762 

197 

0.8443 

197.2 

Tc 

d0  required  by  the  formula:  d0  =  Sdc,  with  Young's  value 
of  dc,  is  0.8736. 

The  formula  appears  then  to  be  correct. 

By  substituting  in  (6)  the  value  of  TV*/3  found  by  combining 
(n)Aand  (14)  there  is  obtained 

(27)  a  =  M((S2  —  S  +  2)/(S  —  2))R(TC—  T)  '/aT/A/  (^  —  dv). 


Table  6  contains   the  results  of  calculating   "a"   by  this 
formula. 


6  —  "a"  BY  FORMULA  (27)  IN  DYNES  FOR  A  GRAM 

Oxygen 
Isopentane  Pentane  (Mathias  and  Onnes) 


t 

a  X  icr12 

t 

a  X  icr13 

t 

a  X  icr12 

1.966 
I-956 
I  .966 
I  .966 

—136.5 
—  30.6 

0 

50 

IOO 
!50 

170 
1  80 

187 

187.8 

22.52 
22.63 

22.54 
22.30 

22.00 

21.83 

22  .OI 

22  .25 
22.73 

Tc 

—123 

—  35-3 

0 

50 

IOO 

150 
1  80 
190 

195 
197 

197.2 

23-15 
23.30 
23-03 
22.84 
22.70 
22.38 
22.48 
22.66 

22.81 
23.51 

Tc 

—  210.4 
—182 

—154-51 
—140.2 

Ether 

—89.2 

+  20 
IOO 

150 
1  80 
190 
193-8 

20.53 
20.34 

19-95 
19.81 
19.90 
19.85 

Tc 

The  Internal  Pressures  of  Liquids  619 

This  formula  gives  remarkably  constant  results  for  the  cal- 
culation clear  to  the  critical  temperature  from  nearly  the 
point  of  solidification.  The  results  are  in  agreement  with 
other  methods  of  calculating  "a"  already  given  or  to  be  de- 
scribed. The  density  values  for  all  except  oxygen  are  those 
of  Timmermans  or  Young. 

3.  Computation  of  "a"  from  van  der  Waals'  Equation  at 
the  Critical  Temperature  assuming  that  bc  =  2V0  =  2Vc/S% 

The  values  for  "a"  computed  by  the  preceding  methods 
from  the  surface  tension  agree  with  those  computed  from  van 
der  Waals'  equation  at  the  critical  temperature  assuming  that 
bc,  the  co- volume,  or  the  real  volume  of  the  molecules,  is  always 
in  all  normal  substances  just  twice  the  volume  at  absolute  zero, 
or  that  bc  ==  2V0.  As  the  volume  at  absolute  zero  is  equal  to 
the  critical  volume  divided  by  S,  where  S  ==  RTC/VCPC, 
bc  =  2VC/S.  Applying  this  to  the  equation,  since  VCPCS  = 
RT,  we  have 

(28)  a  =  (S2  —  S  +  2)T'R2/(S2(S  —  2)Pe);  or 

(29)  a  =  (S2-S  +  2)Pcv;/(S-2). 

Formula  (28)  which  corresponds  to  van  der  Waals'  formula: 
a  --=  2yT'/(64  X  273*  X  Pc),  has  been  used  in  computing 
"a"  in  Table  8.  The  values  thus  obtained  are  practically 
identical  with  those  computed  from  the  surface  tension. 

Formula  (29)  has  already  been  obtained  as  (18). 

4.  The  Computation  of  "a"  from  the  Internal  Latent  Heat 

of  Vaporization 

That  the  foregoing  values  of  "a"  are  correct  is  proved  by 
their  agreement  with  the  values  computed  from  the  internal 
latent  heat  of  vaporization  close  to  the  critical  temperature. 

If  all  the  internal  latent  heat,  I,  was  used  in  overcoming 
molecular  cohesion,  then  the  equation  should  hold 

(30)  X  =  L  —  E  =  a(ijV,~  i/Vw), 

where  L  is  the  total  latent  heat  and  B  the  external  work. 
This  equation  does  not  hold  except  close  to  the  critical  tern- 


620 


Albert  P.  Mathews 


perature,  since  as  we  go  to  lower  temperatures  "a,"  computed 
by  this  formula,  becomes  steadily  larger.  This  is  owing  to 
the  fact  that  some  of  the  latent  heat  is  consumed  in  doing  other 
things  than  in  overcoming  molecular  cohesion,  a  part  probably 
being  rendered  latent  by  an  actual  expansion  of  the  molecules. 
H  is  the  latent  heat  used  in  increasing  the  intramolecular 
energy.  It  vanishes  close  to  the  critical  temperatures.  I 
have,  therefore,  computed  "a"  by  this  formula  within  a  degree 
or  so  of  the  critical  temperature.  At  temperatures  lower  than 
this  "a"  by  this  method  will  be  found  too  large,  but  within  a 
fraction  of  a  degree  of  the  critical  temperature  the  change 
in  the  size  of  the  molecules  is  probably  negligible.  To  find  ^ 
at  this  temperature  I  have  computed  it  from  S.  Young's 
recently  published  data  of  the  liquid  and  vapor  densities 
using  Mills'1  formula  for  the  computation  of  X,  namely, 


7  —  COMPUTATION  OF  "a"  FOR  ONE  GRAM  MOL  FROM  INTERNAL 
HEAT  (NEGLECTING  //) 


Substance 

Distance  from  the 
critical  temperature 

a  X   io-13 

Pentane  (ri) 

-0.05° 

2.108 

Pentane  (iso) 

2.065 

Hexane 

^^     Q 

2.814 

Heptane 

—3-5 

3.616 

Octane  (n) 

—6.2 

4-575 

Hexamethylene 

1  .0 

2-445 

Ether 

—  0.8 

1-945 

Carbon  tetrachloride 

—3-15 

2  .202 

Benzene 

—0.15 

2.  112 

Fluorbenzene 

—6.55 

2.266 

Chlorbenzene 

•  —  89.2 

3.260 

Methyl  formate 

—  0.5 

I-I45 

Methyl  acetate 

—0.7 

1.772 

Methyl  propionate 

-1.4 

2-349 

Ethyl  acetate 

—  i  .0 

2-359 

Propyl  formate    v 

-4-85 

2-395 

Ethyl  propionate 

—2.9 

3-058 

Methyl  butyrate 

—i-3 

2.989 

Methyl  isobutyrate 

-1.05 

2.892 

1  Mills:  Phil.  Mag.,  21,  85  (1911). 


The  Internal  Pressures  of  Liquids  621 

A  =  C(d1/3  —  D!/3).  The  value  of  C  was  the  mean  C  taken 
from  Mills'  recent  paper.  These  values  of  the  internal  latent 
heat  are  very  similar  to  those  obtained  by  Dieterici's  formula 
>i  =  CRT/wd/D.  If  the  internal  latent  heat  is  computed 
using  the  vapor  pressures  computed  by  Biot's  formula  close 
to  the  critical  temperature  too  low  values  are  obtained  as 
Mills  has  pointed  out. 

The  values  for  "a"  for  one  gram  mol  computed  from  near 
the  critical  temperature  are  given  in  Table  7.  Column  2  of 
that  table  shows  how  many  degrees  below  the  critical  tempera- 
ture data  were  taken  for  the  computation.  The  nearer  the 
critical  temperature  the  more  reliable  the  data  should  be. 

(31)  a  =  M(X  —  fi)l(dr—dv). 

It  is  interesting  now  to  see  how  large  /*  is  relative  to  ^  at 
different  temperatures;  that  is,  how  much  of  the  heat  of  vapor- 
ization is  rendered  latent  by  the  expansion  of  the  molecules, 
or  by  an  increase  in  their  rotatory  energy.  By  formula  (31) 
a  =  M(J  —  fi)/(dl  —  dv)\  and  by  (29)  a  =  (S2  —  S  +  2)PCV'A 
(S  —  2) .  Hence  we  have 

(32)  v^—  ft  =  (S2  — S  +  2)PCVX  — ^)/M(S  — 2). 
But  it  was  found  by  Mills  that  X  =  C(d?/3  —  </3)  so  that 

(33)  fi  =  C(d1/*  —  </3>— (S2  —  S  +  2)PcVX  —  dj  /M(S  —  2) . 
The  calculation  of  /£  for  one  gram  mol  of  pentane  by  formula 

(33)  resulted  as  follows : 


i 

fi  X  icr10  ergs 

-273° 

4-25 

+  30 

4.46 

60 

3-51 

IOO 

2.18 

150 

190 

0.62 
—  0.0026 

197.2 

Tc 

At  30°,  therefore,  the  total  latent  heat  for  one  gram  is 
85.76  cals;  the  total  internal  latent  heat,  or  A,  is  78.80  cals.; 


622 


Albert  P.  Mathews 


§" 


X  H)nOi  X 


=  v    \      vo 


M      M      Th< 

O 


N      O      M      10    M      M 

04     CM 


CO  iO  rj- 

O  ^O    i— i 

M  O    CO 

CM  CM     CM 


a 

w 


g 


X 


+  s  — 


1-1    CO  ^  CO 
COCO    <N     rj- 


M     O     >-<     *O   CM     CM 
CM     CM 


S/'A'Xs01  X 


^o  ^  o  o 

ON  co  t^  O    ^  O 
M    O     M    ""3  CM     CM 


The  Internal  Pressures  of  Liquids 


623 


CO 


0 


O    t^^O    Th  ON  iO  t^<O  "O    ONO    10  CM  VO  VO  VO    •^-rt-Tt-rhvo    rJ-'^-'OOO    .H 
GO    M    rt-  ON  M    ONONQ    CM    O    O    CM    Tt-ONONONOOOOOOCO    co  *O  CO  CM    iO    *i 


\O    10  IO 


C4    O 

w  VO 


\O    iO  ON  CS    M    04 
CO  rh  M    o<    04    CO 

vvv     v 


10  ONCO   ON 


OO 

10 


co  co  co  ONCO          O 

C^C^CSCSCN  CO 

VV  V  VV      V 


CM  GO     M  CO  M    ON 

GO    ON  CM  iO  TJ-  O 

•3-  M   o  rt-  CM   O 

CO  Tj-  CS  <N  CM     CO 


w 


CN     O     COCO     O4 

oo    O    ft    CM    co 


Tl-  CM         n-  r<   O 

CO  rt-  CS    (N    CS    CO 


iO  ro  1000    IOOO    iO  10  ON 


cs   cooo  i>.co 


!>•  CO  O 


CM  GO  O    CM    r>-  ri*  CO  CO  IH    M    O    ^"  OO  CO    M    M  OO    CO 
1-1    O  ^O  OO    iO  CM    ^OO  VO    CM    O    ONt^ONO    ONCOIO 


^t-  O   ^  c^    ONGO   T}- 

rj-  M     CM     CN     C4     CS     CO 


ONOO    CS 


CM    co  CO  O  00    ON  ON  ONVO    co  <N 


V 

•a 


-s 


-s 


illrlifllf^^ 

Bj£8.&g3£Ji|i| 

•R'fe'S^i  •S.fe'&'Sw-  -c1 


liiillillllllw 

ffiOWO«OH§<IOOSS 


o  g  g^^^^-B&^ST&'S 


.IS  o  ^ 

£2  ° 

JH  ca  o 

S«g[ -g 

rO  b  a 


624 


Albert  P.  Mathews 


X  H)  Tloi  X 


MD 


s  — 


S  — 


rj-        O  o 

2     £§ 

CS  sS 


S(X 


8 


A 


The  Internal  Pressures  of  Liquids  625 


t^«              H 

"•           Th         VO                    CM 

*          ON         Tf~               ^" 

f*        C 

CM             •< 

5        <N        o             r^ 

i-           CM             CM                    M 

M                t 

O           CM            lO                   CM 

^        O         Tf-              t^ 

00            L 

CM             •< 

\ 

O         CM          ON               IN- 

J-              CM                M                           M 

/       V 

00            C 

CO         H 

5         Th       t^            vO 

•i          co         M                 O 

00            C 
CM             " 

^         -"vh        O               t^ 

^           CM             CM                     M 

co      & 

CO         C 

3                CO              M                          M 

^       10       CM             o 

oo        •• 

CM             •< 

J-           CM             CM                    M 

ON 

00 
CM 

^h        rj-             10 

CO          O! 
CO         C 

D               CO             M                         M 
JN            lO            CM                      O 

00                  H 

CM             " 

•*          ^         O                l*** 

^-           CM             CM                    1-1 

CM             H 

co        C 

•i   "^    O  0^  CM                   O 
3  ^  VO    CM    M                <> 

CM             •< 

J-J  S  K  ?        ^ 

*^  M  OO    io^O     CM     coo"^ 

•     •-...-    o 

*-<    tO   <N     "^  O     CM 

rh  M   CM   r^  CM  N~-^' 


ONO"^  CM 

M 

CO 

CO 

lO   CM     *"*• 

O 

CO 

rt- 

00  QO    ^* 

<* 

0 

j-^ 

CM  ^  —  rf 

CM 

CM 

#            <y 
§            § 

8'    1 

1 

£ 

^   rt 

^ 

Is 

W     o 

{J 

w 

g 

626  Albert  P.  Mathews 

and  fi,  the  heat  rendered  latent  by  an  increase  in  the  intra- 
molecular energy,  is  14.80  cals.  While  the  figure  14.80  is 
undoubtedly  a  little  too  low  it  appears  that  approximately 
one-fifth  of  the  total  internal  latent  heat  goes  within  the  mole- 
cules at  the  fraction  0.313^.  Furthermore,  the  internal 
intramolecular  latent  heat  does  not  increase  much,  if  at  all,  at 
temperatures  lower  than  this.  The  theoretical  latent  heat  at 
absolute  zero  was  calculated  by  Mills'  formula,  and  d0  was 
taken  as  $dc. 

5.  Computation  of  "a"  from  the  Number  of  Valences  and 
Molecular  Weight 

Finally  I  have  calculated  "a"  for  a  gram  mol  by  the  formula  :L 

(34)  a  =  C(M  X  Val)2/3. 

C  is  taken  arbitrarily  as  equal  to  1.259  X  ion.  M  is  the  molecu- 
lar weight,  and  Val  the  numbers  of  valences  per  molecule. 

The  values  computed  in  these  different  ways  are  given  in 
Table  8.  For  the  surface  tension  computations  I  have  taken 
the  data  from  Ramsay  and  Shields,  Ramsay  and  Ashton  and 
Renard  and  Guye.  In  all  cases  when  computing  "a"  by  the 
last  formula  the  valence  of  carbon  has  been  taken  as  4 ;  oxygen 
as  2,  except  in  oxygen  gas,  where  it  is  unity;  nitrogen  as  3, 
except  in  nitrogen  gas  which  has  been  taken  as  monovalent; 
and  hydrogen  as  i .  The  critical  data  of  oxygen  are  accurately 
determined;  for  hydrogen,  the  critical  density  being  uncertain, 
I  have  assumed  S  to  be  3.4,  the  same  as  oxygen ;  in  computing 
nitrogen,  the  critical  density  being  uncertain,  I  took  S  as  3.5 
and  the  density  0.33,  which  is  between  the  values  given  by 
Sarrau  and  Hautefeuille  and  Cailletet.  For  all  substances 
included  in  his  list  Young's  critical  data  have  been  used. 
The  critical  temperatures  and  pressures  of  the  other  substances 
have  been  taken  from  the  Landolt-Meyerhoffer  tables.  Where 
the  critical  density  was  unknown  I  have  been  unable  to  com- 
pute by  formulas  which  involve  that  factor.  In  other  cases 
the  surface-tension  data  or  the  vapor  densities  could  not  be 
found.  Hence  there  are  many  gaps  in  the  table. 

1  Mathews:  Jour.  Phys.  Chem.,  17,  181  (1913). 


The  Internal  Pressures  of  Liquids 


627 


It  will  be  seen  by  an  inspection  of  Tables  8  and  9  that  all 
the  formulas,  i.  e.,  those  from  the  latent  heat;  from  van  der 
Waals'  equation,  assuming  that  bc  is  2VC/S;  from  the  surface 
tension;  from  Young's  formula  and  that  involving  the  molecu- 
lar weight  and  number  of  valences,  give  practically  the  same 
result.  The  confirmation  of  the  values  from  the  surface 
tension  and  van  der  Waals'  equation  by  the  computation  from 
the  latent  heat  close  to  the  critical  temperature  is,  I  think, 
conclusive  evidence  that  these  results  are  correct,  within  the 
limits  of  error  of  the  data  from  which  they  are  computed. 
The  internal  pressures  of  such  liquids  as  benzene  and  ether  are, 
therefore,  about  14  per  cent,  higher  than  have  been  calculated 
by  van  der  Waals'  formula:  a  --=  27^/64  X  2732PC.  As  a 
result  the  co-volume,  or  the  volume  of  the  molecules,  the  value 
"6,"  must  be  taken  larger  both  in  the  liquid  and  vapor  than 
has  been  customary. 

The  values  for  "a"  and  M2K  given  in  my  earlier  papers 
should  be  multiplied  by  i  .085  approximately  to  bring  them  to 
these  new  and  correct  values. 

The  internal  pressures  at  zero  degrees  centigrade  computed 
by  Lewis,  by  the  method  of  van  der  Waals  and  by  formula 
(7)  compare  as  follows  (Table  10)  : 


10  —  INTERNAL  PRESSURES  IN  ATMOSPHERES  AT  ZERO  DE- 
GREES 


Lewis 

v.  d.  Waals 

Formula  (7) 
Surface  tension 

Ethyl  acetate 

2466 

2261 

2507 

Ether 

1932 

1723 

1986 

Carbon  tetrachloride         2518         2205 

2637 

Carbon  bisulfide                 2917         3363 

3937 

Benzene 

2639 

2494 

2946 

Toluene 

2847 

2228 

2534 

m-Xylene 

2815         2068  (10°) 

2286  (10°) 

The  values  obtained  from  the  surface  tension  and  from  the 
latent  heat  of  expansion  as  computed  by  Lewis,  agree  pretty 
well  except  in  the  case  of  carbon  bisulphide;  they  are  widely 


628  Albert  P.  Mathews 

different  from  those  computed  by  Walden  from  Stefan's  con- 
clusion, Walden 's  values  being  in  fact  about  two-thirds  of 
my  values.  The  figures  given  for  the  internal  pressures  of 
liquids  by  Walden,  Davies,  and  Traube  are  certainly  far  too 
low  and  are  erroneous. 

Summary 

The  internal  pressures  of  liquids,  or  rather  the  value  "a" 
of  van  der  Waals'  equation,  has  been  computed  from  the 
surface  tension,  assuming  that  the  depth  of  the  surface  layer 
is  (TC/TC — T))f/3  molecular  diameters;  from  the  law  of  Eotvos 
and  T.  Young;  from  van  der  Waals'  equation,  assuming  that 
bc  is  always  2VC/S,  S  being  equal  to  RTC/VCPC;  from  the  in- 
ternal latent  heat  of  vaporization  close  to  the  critical  tempera- 
ture, and  from  the  molecular  weight  and  the  number  of  va- 
lences. All  of  these  methods  give  practically  the  same  results. 
The  values  of  "a"  thus  computed  are  constant  in  the  case  of 
pentane  and  ether  over  a  wide  range  of  temperature,  indicating 
that  barring  association  "a"  is  constant;  the  values  are  uni- 
formly higher  than  those  computed  by  others  with  the  excep- 
tion of  some  computed  recently  by  Lewis  from  the  latent 
heat  of  expansion  of  liquids.  The  values  recently  given  by 
Traube,  Walden  and  Davies  are  too  low  and  incorrect  in  other 
ways.  The  results  confirm  my  conclusion  that  the  molecular 
cohesion  is  a  function  of  the  molecular  weight  and  the  num- 
ber of  valences  in  the  molecule.  The  formula:  a  = 
27^/64  X  2732PC  gives  values  about  14  per  cent,  too  low 
for  ordinary  substances  and  very  much  too  low  for  simple 
diatomic  gases.  It  should  be  replaced  by  the  formula  a  = 
(S2  — S  +  2)T*R2/(S2(S  — 2)PC).  These  results  show,  also, 
that  Stefan's  conclusion  that  half  the  work  in  vaporization  is 
done  in  moving  a  particle  into  the  surface  is  incorrect.1 

University  of  Chicago 

1  APPENDIX. — By  combining  (23)  and  (26)  we  have  the  following  formulas 
for  calculating  S  and  dc.     M  is  the  molecular  weight: 

(35)  S2  =  (dt  —  ^)T4/3/(Tc  —  T)V3MPC 


(36)  dc  =  MPc(de — ck>)/RTc/3(Tc  —  T)x/3. 


THE  QUANTITY  OF  RESIDUAL  VALENCE  POSSESSED 
BY  VARIOUS  MOLECULES 


BY   A.    P.    MATHEWS 

All,  or  nearly  all  molecules  .possess  some  power  of  com- 
bining with  molecules  of  the  same  or  different  kinds.  This 
combining  power  is  called  the  residual  valence,  or  affinity, 
of  the  molecule.  Thus  ammonia,  NH3,  will  unite  with  water 
or  acids,  a  molecule  of  hemoglobin  with  oxygen,  glucose  and 
probably  all  salts  with  water  when  they  dissolve  in  it,  and 
other  examples  of  this  power  of  molecular  union  might  be 
given. 

The  importance  of  residual  valence  to  the  molecule  is 
generally  recognized.  It  is  probable  that,  with  the  possible 
exception  of  ionic  reactions,  these  molecular  unions  precede, 
and  are  a  necessary  condition  for,  most  chemical  interactions 
between  molecules;  for  molecules  do  not  seem  to  affect  each 
other  by  simple  contact,  but  only  when  they  are  united  into 
a  new  molecule  by  chemical  bonds.  It  would  seem  that  it  is 
only  when  they  are  thus  united  that  the  atoms  of  two  mole- 
cules are  able  to  interchange  and  undergo  those  rearrange- 
ments resulting  in  the  birth  of  new  molecular  species. 

The  importance  of  residual  valence  makes  it  desirable  to 
know  how  much  of  it  is  possessed  by  each  species  of  molecule. 
Since  it  is  possible  that  this  amount  may  not  always  be  the 
same  even  for  the  same  species  of  molecule,  a  method  must 
be  used  in  determining  the  average  amount  which  will  examine 
the  molecular  system  without  disturbing  it.  For  example 
not  all  the  molecules  of  carbon  dioxide  may  be  in  a  condition 
to  unite  with  water  at  the  same  instant.  Many  facts  indicate 
that  of  all  the  molecules  of  oxygen  in  the  air  only  a  few,  at  any 
instant  of  time,  are  in  a  condition  to  unite  with  oxidizable 
substances.  The  number  possessing  residual  valence  is  small. 
This  changing  molecular  condition  seems  analogous  to,  and 
is  very  possibly  essentially  identical  with,  the  varying  condi- 
tion of  atoms  of  radium  which  only  occasionally  become 


Residual  Valence  of  Various  Molecules  475 

radioactive  and  decompose.  It  is  not  impossible,  on  the 
electronic  theory  of  valence,  to  ascribe  the  acquiring  of  addi- 
tional or  residual  valence  by  the  atoms  of  molecules  to  internal 
rearrangements  of  the  electrons  within  the  atoms,  similar 
to  that  rearrangement  which,  in  radioactive  substances,  leads 
to  an  explosion  of  the  atom. 

The  method  I  have  used  to  determine  the  quantity  of 
residual  valence  is  a  physical  one,  based  on  the  cohesion  of 
molecules.  While  the  method  is  not  very  accurate  at  present, 
owing  to  several  doubtful  points  in  the  calculations,  it  probably 
places  the  molecules  in  the  order  in  which  they  occur  when 
arranged  according  to  the  amount  of  average  residual  valence 
they  possess;  and  it  will  become  more  precise  as  the  critical 
data  are  more  accurately  known  and  the  cohesion  or  internal 
pressure  more  accurately  determined.  The  method  is  as 
follows :  The  internal  or  cohesive  pressure  of  a  fluid  is  rep- 
resented by  the  value  a/V2  of  van  der  Waals'  equation. 
In  this  expression  V2  represents  how  the  cohesional  attraction 
varies  with  the  distance;  and  "a"  is  the  "mass"  factor  of  the 
attraction.  Now  "a"  includes  the  factor  N2,  N  being  the 
number  of  molecules  in  the  volume  V,  and  if  "a"  is  divided 
by  N2  then  the  quotient  represents  the  "mass"  factor  of  the 
cohesional  attraction  of  two  molecules  and  it  may  be  written 
M2K  to  correspond  with  the  mass  factor  of  the  gravitational 
attraction,  m2k,  in  which  "m"  is  the  gravitational  mass  and 
"k"  the  gravitational  constant.  The  relationship  was  found1 
that  M2K  is  proportional  to  the  two-thirds  power  of  the 
product  of  the  molecular  weight  by  the  number  of  valences 
in  the  molecule,  or  M2K  =  C(Wt.  X  Val.)2/'.  How  accu- 
rately this  relationship  holds  is  shown  in  Table  I  in  which  the 
value  of  "a"  which  is  of  course  proportional  to  M2K,  and 
is  the  mean  value  computed  from  various  formulas,  is  com- 
pared with  the  value  of  "a"  computed  from  the  molecular 
weight  and  the  number  of  valences.  The  method  of  com- 
puting "a"  was  given  in  another  paper.2 


1  Mathews:  Jour.  Phys.  Chem.,  17,  181  (1913). 

2  Mathews:  Ibid.,  17,  603  (1913)- 


A.  P.  Mathews 


TABLE  I 

Comparison  of  "a"  computed  from  the  critical  data,  etc., 
with  "a"  computed  from  the  molecular  weight  and  valence.  The 
figures  represent  dynes  for  gram  mol  amounts,  multiplied  by  io~12 


Substance 

Mean 
value 
of  "a" 

a  =  C(Wt.  X  Val.)Vs 
(C  =  1.259  X  ion) 

Difference 
Actual 

Difference 
Percent 

H2 

0.311 

0.317 

—  O.O06 

-1.89 

N2 

1.836 

1.842  (Val.  =  2) 

—  0.006 

—0.31 

02 

1.984 

2.014  (Val.  =  2)     —  0.030 

-i-5 

w-Pentane 

22.07 

21  .96 

+0.1  1 

+0.5 

^-Pentane                       21.41 

21  .96 

—0-55 

2  .2 

w-Hexane 

28.10 

27.71 

+0.39 

+  1-38 

Heptane 

34-82 

33-8o 

+  i  .02 

+  3.06 

Octane 

41.94 

40.17 

-1.77 

+4-4 

Diisobutyl 

40.01 

40.17 

-^0.16 

—0.4 

Ether 

19.94        20.46 

—0.72 

—0.32 

Benzene 

21-95 

22.  19 

—0.24 

—  o.  ii 

Chlor-benzene 

23.26 

22.94 

+0.32 

+0.14 

Toluene 

28.12 

27.97 

+0.15 

+0.50 

Metaxylene 

34.08 

34.06 

0.02 

+0.06 

Methyl  formate 

12.04 

12.25 

—  0.21 

—1-7 

Methyl  acetate 

17.  12 

17.42 

—0.30 

—i  .  i 

Methyl  propionate 

22.49 

22.96 

—0.47 

2.0 

Ethyl  acetate 

22.84 

22.96 

—  0.  12 

—0-5 

Propyl  formate 

23-I3 

22.96 

+  0.17 

+0.72 

Methyl  butyrate           29  .  53 

28.84 

+0.69 

+2.4 

Methyl  iso-butyrate     28.27 

28.84 

--0.60 

—  2.  I 

Propyl  acetate            ;  28.95 

28.84 

+  0.08 

+0.3 

Ethyl  propionate          28.92 

28.84 

+  0.05 

+  0.2 

SnCl4                              32.58 

32.  58  (Val.  =  16) 

^O.OO 

=4=0.00 

From  the  equation  a  =  C(Wt.  X  Val.)2/8,  if  M2K,  or 
"a,"  can  be  determined,  and  if  C  and  the  molecular  weight 
are  known,  the  total  number  of  valences  in  the  molecule  can  be 
calculated.  If  from  this  total  number  of  valences  there  be 
subtracted  the  number  which  is  known  to  exist  in  the  mole- 
cule on  the  basis  that  hydrogen  is  univalent,  oxygen  bivalent, 
carbon  quadrivalent  and  so  on,  the  remainder  may  be  sup- 
posed to  constitute  the  average  amount,  or  number,  of  extra 
or  residual  valences  which  the  molecule  possesses.  It  is  this 
number  which  has  been  determined  in  this  paper. 


Residual  Valence  of  Various  Molecules  477 

Granting  that  this  number  really  represents  the  residual 
valence,  the  accuracy  with  which  it  can  be  determined  will 
depend  on  the  accuracy  with  which  M2K,  C,  the  molecular 
weight  and  the  number  of  valences  reaching  between  the 
atoms  can  be  determined.  The  molecular  weight  may  be 
assumed  to  be  normal  for  non-associating  substances  at  the 
critical  temperature;  and  we  have  to  assume  that  the  number 
of  valences  between  the  atoms  are  those  which  chemists 
usually  assign  to  these  elements.  The  determination  of  the 
constant  C,  however,  is  more  difficult.  It  could  be  deter- 
mined empirically  if  M2K  was  known  accurately  for  any 
substance  of  which  the  valence  is  fixed  and  certain.  Hydrogen 
is  the  only  element  with  an  unchanging  valence,  but  un- 
fortunately the  critical  pressure  of  hydrogen  is  uncertain. 
Moreover,  it  cannot  be  assumed  that  the  valence  of  hydrogen 
is  exactly  unity.  There  are  several  indications  that  a  mole- 
cule of  hydrogen  has  some  residual  valence  although  it  is 
certainly  small  in  amount.  One  such  indication  is  the  solu- 
bility of  hydrogen  in  water.  At  the  same  pressure  and  tem- 
perature more  molecules  of  hydrogen  dissolve  in  water  than  of 
helium,  and  hydrogen  is  half  as  soluble  as  nitrogen  which  al- 
most certainly  has  residual  valence.  If  solubility  involves 
residual  valence,  as  it  may,  this  means  that  hydrogen  would 
have  some  residual  valence.  Its  solubility  in  platinum  may 
be  interpreted  in  the  same  sense.  The  catalytic  reducing 
action  of  platinum,  nickel  or  other  metals  or  metallic  oxides 
in  a  hydrogen  atmosphere  is  interpreted  by  Sabatier1  to  mean 
that  a  chemical  union  of  the  reacting  substances  occurs. 
Armstrong,2  too,  has  expressed  the  opinion  that  hydrogen 
has  a  small  amount  of  residual  valence.  For  these  reasons 
we  cannot  accurately  determine  C  from  hydrogen.  Never- 
theless I  have  calculated  M2K  and  C  for  hydrogen  to  show 
what  the  value  of  C  would  be  if  hydrogen  were  univalent. 


1  Sabatier:  Nobel  Prize  Address,  p.  9,  et  seq.;  Les  Prix  Nobel  en  1912; 
La  Methode  d'Hydrogenation  directe  par  Catalyse. 

2  Armstrong:    "Valency,"    Encyclopaedia  Britannica,    nth  Ed.,  27,  848 
(1911). 


478  A.  P.  Mathews 

Using  the  critical  data  of  Tc  =  32.3  and  P0  13  atmospheres 
as  found  by  Olszewski;  and  dc  as  0.033  as  determined  by 
Dewar,  the  critical  coefficient  S,  where  S  =  RTC/PCV0  is 
equal  to  2.860.  This  value  of  S  is,  however,  much  lower  than 
that  of  any  other  substance.  Thus  for  O2,  S  is  3.5;  for  N2, 
3.6;  for  N2O,  3.4  and  even  for  helium  it  is  3.13  according  to 
Onnes.  It  is  probable  then  that  2.86  is  too  low.  The  critical 
temperature  and  pressure  have  recently  been  determined  by 
Buller1  who  finds  Tc  =  31.95;  Pc  =  n.  With  these  values 
and  dc  =  0.033  S  computes  3.903,  which  is  higher  even  than 
such  complex  substances  as  octane  and  is  clearly  too  high. 
If  S  is  calculated  by  my  formula  which  gives  a  result  within 
1-2  percent  in  most  cases,  namely,  S2  =  R(Wi  -  -  d^T^3/- 
(Tc  — T)1/3MP0  using  Buller's  values  for  Pc  and  Tc  and 
taking  d\  as  that  of  hydrogen  at  the  melting  point  [ — 258.9° 
(Travers)]  as  0.086  (Dewar)  and  disregarding  the  value  of  dv 
at  that  temperature  then  S  is  computed  as  3.517.  If  Pc  were 
11.5  atmospheres,  and  the  uncertainty  is  at  least  half  an 
atmosphere,  S  would  be  3.365.  I  believe  S  of  hydrogen  may 
be  taken  as  approximately  that  of  oxygen  or  as  3.4.  If  S 
is  assumed  to  be  3.4  then  with  Pc  n  and  dc  0.033, 
a  =  (S2  —  S  +  2)/(S  —  2)  PCV2C  =  0.301  X  io12.  Dividing 
this  by  N2  where  N  =  6.062  X  io23,  M2K  for  hydrogen  would 
be  8.191  X  io~37  from  which  C  is  found  to  be  3-23  X  io~37. 
If,  however,  S  =  3.4  and  Pc  13,  then  "a"  would  be  0.317  X  io12, 
M2K,  8.626  X  io- 37  and  C  would  be  3-45  X  io~37.  Since 
from  Buller's  results  it  is  probable  that  Pc  should  be  lower  than 
13  atmospheres,  the  value  for  M2K  is  probably  not  far  from 
correct  so  that  C  should  be  very  nearly  3.23  X  io~37. 

Another  simple  substance  from  which  a  calculation  of 
C  might  be  made  is  methane,  since  the  amount  of  its  residual 
valence  is  certainly  small  and  the  total  number  of  valences 
per  molecule  is  very  nearly  8.  Unfortunately  the  critical 
density  of  methane  is  unknown  and  Tc  and  Pc  have  not  been 
recently  determined.  However,  if  Tc  is  191.2  and  Pc  is  54.9 


1  Buller:  Phys.  Zeit.,  14,  860-2  (1913). 


Residual  Valence  of  Various  Molecules  479 

(Olszewski)  and  if  S  be  calculated  by  the  formula  already 
given  using  the  value  of  the  density  of  the  liquid  at  — 164° 
as  0.466  and  disregarding  the  vapor  density,  S  computes  to 
be  3.318  which  is  probably  not  far  wrong.  From  this  "a"  is 
found  by  the  formula  given  above  to  be  3.025  X  io12,  M2K  is 
8.232  X  io~36  and  C  is  found  to  be  3.24  X  io~37  which  is  al- 
most the  same  value  as  that  computed  from  hydrogen. 

The  critical  data  of  oxygen  are  known,  but  the  calculation 
shows  clearly  that  oxygen  is  monovalent  in  the  elemental  form, 
there  being  but  two  valences  in  the  molecule.  This  un- 
expected conclusion  makes  it  impossible  to  use  oxygen  for  the 
determination  of  C  until  it  can  be  shown  from  independent 
sources  that  oxygen  in  the  elemental  form  is  really  mono- 
valent. There  is  some  residual  valence  also.  But  if  the 
residual  valence  be  disregarded  and  two  valences  only  be 
postulated  in  the  molecule,  the  value  of  C  would  be  3.43  X 
io-37. 

The  mean  value  of  C  determined  from  all  the  substances 
in  Table  VIII  in  my  former  paper  was  3-45  X  io~37,  if  Milli- 
kan's  value  of  the  number  of  molecules  in  a  gram  mol.,  namely 
6.062  X  io23,  is  used  in  the  computation.  Since  in  this 
calculation  of  C  the  molecules  were  not  supposed  to  have 
residual  valence,  it  is  clear  that  an  allowance  for  the  presence 
of  this  valence  would  have  the  effect  of  lowering  C,  so  that 
its  true  value  must  be  somewhat  less  than  340  X  io~37. 

A  way  in  which  C  can  be  independently  determined  was 
suggested  by  the  relation  between  cohesion  and  gravitation.1 
In  the  formula  M2K  =  C(Wt.  X  Val.)2/>  it  is  evident  that 
M2K  is  proportional  to  the  2/3ds  power  of  the  gravitational 
mass  of  a  molecule  and  when  weight  and  valence  are  unity 
M2K  =  C.  It  occurred  to  me  that  under  these  circumstances 
C  might  very  possibly  be  nothing  else  than  the  factor 
(w2&)2/3  of  a  molecule  of  unity  molecular  weight.  In  this 
case  "m"  is  the  gravitational  mass  of  such  a  molecule  and 
"k"  the  gravitational  constant.  A  computation  of  (m2k)2/1 
using  Millikan's  recent  determination  of  the  number  of  mole- 

1  Mathews:  Jour.  chim.  phys.,  1914* 


480  A.  P.  Matkews 

cules  in  a  gram  mol,  gave  the  result  (w2&)2/3  =  3.20  X  io~37 
which  is  very  close  to  the  figures  already  obtained  from 
methane  and  hydrogen,  and  somewhat  less,  as  it  ought  to  be, 
than  the  mean  value  of  3.45  X  io~37  which  was  obtained  when 
residual  valence  was  disregarded.  In  view  of  these  facts  I 
believe  we  may  assume  that  3.201  X  io~37  is  the  real  value 
of  C,  although  the  theoretical  basis  of  this  relationship  is  still 
lacking,  and  proceed  with  the  calculation  of  the  total  valence 
of  a  molecule  on  that  assumption. 

The  value  of  M2K  is  less  satisfactory.  It  is  here  that  the 
main  uncertainty  of  the  calculation  lies.  As  I  have  already 
discussed  the  methods  of  calculating  this  value  in  my  paper 
on  the  internal  pressures  of  liquids  I  will  not  go  into  the 
question  at  this  time  further  than  to  point  out  two  or  three 
considerations  bearing  on  the  probable  accuracy  of  those 
figures.  In  all  the  formulas  for  "a"  which  have  so  far  been 
proposed  certain  assumptions  have  been  made.  The  one 
ordinarily  made  in  van  der  Waals'  method  of  computing  "a" 
is  that  bc  =  Vc/3-  In  the  various  methods  I  have  proposed 
for  the  computation  quite  different  assumptions  have  been 
made  in  the  different  formulas,  but  nevertheless  these  formulas 
have  all  given  results  which  are  not  widely  different  if  the 
uncertainty  of  some  of  the  experimental  data  are  considered. 
Nevertheless,  the  formulas  do  not  always  give  exactly  the  same 
values  as  they  should  if  all  the  assumptions  and  data  were 
rigorously  correct.  The  computation  of  the  cohesion  from  the 
latent  heat  of  vaporization  should  give  a  correct  result  since 
the  assumptions  made  here  are  less  radical  than  in  any  of  the 
other  methods.  Now  this  method  generally  gives  a  value  for 
"a"  lower,  in  some  cases  5  percent  lower,  than  that  com- 
puted from  the  critical  data.  But  I  have  not  been  able  to 
attach  more  importance  to  this  deviation  for  the  reason  that 
the  computation  must  be  made  close  to  the  critical  tempera- 
ture, within  a  fraction  of  a  degree  of  it,  and  a  very  slight  error 
in  the  difference  of  the  vapor  and  liquid  densities  would  make 
a  very  large  error  in  "a."  That x the  formulas  proposed  for 
"a"  are  possibly  not  entirely  accurate  may  be  shown  also 


Residual  Valence  of  Various  Molecules 


481 


by  the  following  circumstance:  From  the  formula 
a  =  ((S2  S  +  2)/(S  2))P«V*  and  the  formula 

a  =  M((S2  —  S  +  2)/(S  —  2))RT2/'(TC  -  -  T)1/'/^  —  </.)  we 
have  V'  =  MR(TC  -  -  T)'/>T2/V(di  —  d,)Pe.  If  now  we  com- 
pute dc  of  oxygen  by  this  formula  from  the  densities  of  liquid 
and  vapor  oxygen  found  by  Mathias .  and  Onnes,  we  find 
indeed  a  constant  value  for  dc,  but  a  density  nearly  3  percent 
higher  than  that  computed  by  the  rectilinear  diameter  law, 
as  follows: 

TABLE  II 

Computation  of  the  critical  density  of  oxygen  from  the  densities 
at  different  temperatures,  t 


— 118.8°  0.4413 

—120.4  0.4428 

-140.2  0.4437 

—154.51  0.4427 

dc  computed  by  Mathias  and  Onnes  by  the  rectilinear  diameter 
law  was  0.4299. 

The  deviation  with  pentane  was  in  the  opposite  direction. 
dc  was  found  by  S.  Young  to  be  0.2323.  If  it  is  calculated 
by  the  foregoing  method  from  Young's  density  figures  we  have 


o          0.2235 
160          0.2265 

In  this  case  the  result  was  about  3  percent  too  low. 

With  octane  the  computed  and  found  values  agree  very 
well,  as  follows,  using  Young's  density  figures  at  various 
temperatures. 


/ 

dc 

0° 

0.2319 

60 

0.2324 

120 

0.2336 

1  60 

0.2348 

190 

0.2352 

230 

0.2372 

482 


A.  P.  Mathews 


The  density  values  show  a  tendency  to  advance.  The  mean 
value  of  about  0.2330  is  very  close  to  that  determined  by 
Young  of  0.2327. 

The  critical  density  calculated  for  various  other  sub- 
stances from  the  liquid  and  vapor  densities  resulted  as  follows 
when  compared  with  the  found  values : 


Substance 

Temperature  and  density  from                   dc 
which  calculation  made                |    Calculated 

dc 
Found 

Benzene 

0° 

di  =  0.90006;  dv  =  0.00012 

0.3019 

0.3045 

Fl-benzene 

0° 

di  =  1.04653 

0-3495       0.3541 

Br-benzene 

0° 

di  =  1.52182 

0.4804       0.4853 

CO2 

0° 

d\  =  0.914;      dv  =  0.096 

0.4749 

0.46 

CCU 

ou 

di  =  1.63255 

0.5569       0.5576 

Ethyl  ether 

0° 

d\  =  0.7362;    dv  =  0.000827 

0.2605       0.2625 

60° 

di  =  0.66580;  dj,  =  0.006771 

0.2622 

The  foregoing  figures  show  that  the  formula  used  for  the 
calculation  of  dc,  which  was  derived  from  two  of  the  formulas 
used  in  the  calculation  of  ''a,"  gives  results  which  agree 
generally  within  i  percent  of  the  values  of  the  critical  density 
determined  by  experiment,  but  in  some  cases  there  is  a  devia- 
tion of  about  3  percent.  We  may,  I  think  estimate  the  un- 
certainty in  the  value  of  "a"  and  hence  of  M2K,  as  not  more 
than  2-3  percent. 

The  formula  which  I  have  chosen  for  the  calculation  of 
the  value  of  ua"  is  that  which  is  based  on  the  assumption  that 
the  value  of  bc  is  2VC/S.  This  formula  is :  a  =  ((S2  —  S  +  2)/- 
(S  --  2))PCVJ.  This  equation  involves  only  the  critical  data 
and  may  be  applied  to  the  largest  number  of  substances. 

While  the  calculation  of  the  total  valence  of  the  molecules 
is  thus  subject  to  these  uncertainties,  it  is  probable  that  the 
substances  are  arranged  in  their  proper  order  of  the  amount  of 
residual  valence  and  that  the  error  in  the  total  valence  of  the 
molecule  is  not  more  than  5  percent  at  the  outside.  The  re- 
sults are  given  in  Table  III.  The  values  of  "a"  are  taken 
from  column  4  of  Table  VIII  of  my  paper1  on  the  internal 
pressures  of  liquids. 

1  Mathews:  Loc.  cit.,  p.  622. 


Residual  Valence  of  Various  Molecules 


483 


TABUS  III 
Amount  of  residual  valence 


I 

Substance 

II 
Formula 

III 

Theoretical 
No.  of  val- 
ences 

IV 
Total  No.  of 
valences  by 
formula 
a=C1(Wt.XVal.)2/' 

V 
Resid- 
ual 
valence 

Hydrogen 

H2 

2 

2.195 

O.IQ5 

Oxygen 

02 

2 

2.195 

0.195 

Nitrogen 

N2 

2 

2.197 

0.197 

Nitrous  oxide 

N20 

4(?) 

6.765 

2.765 

Kthylene 

C2H4 

12 

12.904 

0.904 

n-Pentane 

C5Hi2 

32 

36.59 

4-59 

z-Pentane 

C5Hi2 

32 

35-95 

3-95 

w-Hexane 

CeHu 

38 

43-42 

542 

Diisopropyl 

C6H14 

38 

42.41 

4.41 

Heptane 

CrHie 

44 

50.89 

6.89 

n-Octane 

C8Hi8 

50 

59.08 

9.08 

Diisobutyl 

C8H18 

50 

56.30 

6.30 

Ether 

C4H100 

28 

30.45 

2-45 

Carbon  tetra-chloride 

CC14 

16  (Cl  -  3") 

20.28 

4.28 

Benzene 

C6H6 

30 

33-70 

3.70 

Chlor-benzene 

C6H5C1 

32 

36.40 

4.40 

Methyl  formate 

C2H402 

16 

18.12 

2.12 

Ethyl  formate 

C3H602 

22 

24-39 

2-39 

Methyl  acetate 

C3H602 

22 

23.52 

1.52 

Methyl  propionate 

C4H802 

28 

29-38 

1.38 

Ethyl  acetate 

C4H802 

28 

29.20 

1.  2O 

Propyl  formate 

C4H802 

28 

31.16 

3.16 

Methyl  butyrate 

C5Hi002 

34 

36.11 

2.  II 

Methyl  iso-butyrate 

C5Hi002 

34 

35-30 

1.30 

Propyl  acetate                CsHioC^ 

34 

36.05 

2.05 

rt 

Ethyl  propionate 
Stannic  chloride 

C6Hi002 
SnCl, 

16  (Cl  =  3) 

35-80 
17.68 

1.  80 

1.68 

Carbon  bisulfide 

CS2 

16  (S  =  6) 

15-94* 

— 

Methane 

CH4 

8 

8.15 

0.15 

*  "a"  computed  from  the  surface  tension. 

These  figures  speak  for  themselves,  but  a  word  of  com- 
ment may  be  made  on  some  of  them.  It  seems  probable 
from  the  greater  solubility  in  water  of  oxygen  and  nitrogen 
than  hydrogen,  that  the  average  residual  valence  of  a  molecule 


1  C  =  3.20  X  io~37  X  N2. 


484  A.  P.  Mathews 

of  hydrogen  gas  is  somewhat  lower  than  the  figures  indicate. 
In  the  series  methane,  ethylene,  pentane,  hexane,  heptane  and 
octane  the  residual  valence  is,  respectively,  0.15,  0.9,  4.6,  5.42, 
6.89,  9.05.  In  other  words,  the  residual  valence  increases 
with  the  number  of  carbon  atoms  as  Armstrong  has  already 
inferred  it  should  do.  If  0.15  be  considered  as  the  average 
amount  of  residual  valence  of  a  carbon  atom  when  united 
with  hydrogen  and  if  the  amount  of  residual  valence  increases 
proportional  to  the  square  of  the  number  of  carbon  atoms,  we 
should  have  R.  Val.  =  n2  0.15,  n  being  the  number  of  carbon 
atoms.  By  this  formula  the  number  of  residual  valences 
in  the  series  mentioned  should  be,  respectively,  0.6  for  ethylene, 
3.75  for  pentane,  5.40  for  hexane,  7.35  for  heptane,  and  9.60 
for  octane.  These  values  are  not  very  different  from  those 
actually  found.  This  relationship  does  not  hold  for  the 
esters. 

Another  fact  may  be  noticed,  namely,  that  the  differences 
between  the  total  number  of  valences  in  the  various  groups  of 
esters  is  very  nearly  the  theoretical  number.  Thus  between 
methyl  formate  and  methyl  acetate  a  difference  of  six  valences 
is  required.  5.40  was  the  difference  found.  If  we  take  the 
average  of  the  total  number  of  valences  found  in  the  two 
esters  of  the  formula  C3H6O2  it  is  23.95.  This  is  5.75  valences 
more  than  methyl  formate  has  and  is  almost  exactly  six 
less  than  the  next  higher  homologues  of  the  formula  C4H8O2, 
of  which  the  average  number  of  valences  found  was  29.91. 
This  in  its  turn  is  again  5.79  (required  6)  valences  less  than 
the  average  of  the  next  higher  group  of  the  formula  C5Hi0O2. 
Theoretically,  there  should  be  a  difference  of  32  valences  be- 
tween the  molecule  of  hydrogen  and  a  molecule  of  the  formula 
C5Hi0O2,  whereas  the  method  actually  shows  a  difference  of 
33.62.  It  is  certainly  reasonable  to  suppose  that  this,  differ- 
ence from  the  theoretical  is  to  be  ascribed  to  the  larger  amount 
of  residual  valence  possessed  on  the  average  by  a  molecule 
of  the  ester  as  compared  with  hydrogen. 

In  the  case  of  the  chlorine  compounds  I  have  assumed 
that  the  valence  of  chlorine  is  three.  The  reason  for  this  is 


Residual  Valence  of  Various  Molecules  485 

that  I  have  not  been  able  to  find  any  chlorine  compounds 
which  show  chlorine  to  have  a  lower  valence  than  this.  It 
might  be  assumed  that  these  three  valences  were  composed 
of  one  chief  and  two  residual  valences.  In  that  case  one 
should,  of  course,  make  the  residual  valence  of  chlor-benzene 
6.40  instead  of  the  value  4.40  which  I  have  indicated.  Another 
reason  why  I  have  not  counted  these  two  valences  of  chlorine 
as  residual  valences  is  that  these  chlorine  compounds  are  non- 
associating  compounds,  or  at  any  rate  they  associate  very 
little.  Hence  the  valences,  sixteen  in  number,  found  in 
carbon  tetra-chloride  are  probably  not  free  residual  valences, 
in  the  sense  that  they  are  valences  in  an  active  form  but  not 
saturated  in  the  molecule,  but  they  must  be  saturated  in  the 
molecule.  On  the  other  hand,  the  excess  of  4.28  valences 
found  above  the  calculated  amount  may  or  may  not  be  in 
part  saturated  within  the  molecule. 

It  is  evident  then  that  the  determination  of  the  residual 
valence  by  this  method  of  subtracting  the  theoretical  number 
from  the  total  number  found  is  open  to  these  serious  sources 
of  uncertainty.  All  that  can  be  claimed  for  the  method  at 
this  time  is  that  it  gives  a  method  of  calculating  the  total 
valences  and  thus  estimating  the  residual  valence,  and  that  so 
far  as  indications  go  in  the  hydrocarbons  and  the  esters  the 
compounds  are  at  least  arranged  in  the  order  in  which  they 
would  be  placed,  judging  from  their  reactions,  if  arranged 
according  to  the  amount  of  residual  valence  they  possess. 
I  hope  that  methods  will  be  found  to  differentiate  more  clearly 
between  the  valences  extending  between  the  atoms  and  those 
additional  valences  extending  outward  from  the  atoms  making 
the  residual  valence  proper. 

It  is  still  too  early  to  attempt  to  correlate  the  amount 
of  residual  valence  with  the  solubility  of  compounds.  It 
is  at  least  possible  that  in  solubility  other  factors  than  the 
number  of  valences  come  into  play.  The  attraction  between 
the  molecules  of  solvent  and  solute  may  involve  the  factors 
which  have  been  shown  to  influence  cohesion,  namely,  molec- 
ular weight  and  number  of  valences,  as  well  as  the  amount  of 


486  A.  P.  Mathews 

residual  valence;  it  may  also  involve,  of  course,  the  amount 
of  dissociation  of  the  aggregates  formed  by  cohesion  or  residual 
valence.  It  is  probable,  since  the  atomic  unions  are  as  a  rule 
far  more  stable  than  the  cohesive,  the  chemical  attraction 
between  the  atoms  being  of  an  electro-static  kind,  that  the 
union  between  solvent  and  solute  due  to  the  residual  valence 
is  of  far  more  importance  than  that  of  a  cohesional  nature, 
just  as  the  cohesional  attraction  is  of  vastly  greater  importance 
than  the  gravitational  attraction;  and  there  are  not  lacking 
indications  that  residual  valence  plays  a  very  important  part 
in  solubility.  I  may  mention  in  this  connection  the  series 
helium  to  xenon  already  discussed  elsewhere;  the  great  dis- 
solving power  of  associated  as  contrasted  with  non- associated 
liquids,  shown  by  the  solvent  powers  of  water;  the  less  asso- 
ciation of  associating  substances  when  dissolved  in  associa- 
ting solvents  as  compared  with  their  state  in  non-associating 
solvents;  the  greater  solubility  of  such  gases  as  hydrogen 
sulphide,  ammonia,  sulphur  dioxide  which  have  greater 
residual  valence  than  nitrogen,  hydrogen  and  oxygen,  and 
the  fact  that  they  are  known  to  combine  with  water,  and  so  on. 
The  residual  valence  is  hardly  ever  found  to  be  a  whole 
number.  The  probable  explanation  of  this  is  that  the  number 
found  represents  only  the  average  amount  of  residual  valence 
possessed  by  the  molecules.  It  is  probable  that  the  residual 
valences  open  up  in  pairs,  one  positive  and  one  negative, 
but  that  at  any  instant  of  time  only  a  few  molecules  have  them 
open,  so  that  the  average  amount  possessed  by  each  mole- 
cule may  appear  to  be  a  fraction. 

Summary 

The  amount  of  residual  valence  of  a  number  of  non- 
associating  liquids  and  gases  has  been  computed  by  sub- 
tracting from  the  total  number  of  valences  which  the  mole- 
cule possesses,  as  shown  by  its  cohesion,  the  number  which 
there  is  reason  to  believe  extend  between  the  atoms  of  the 
molecule.  The  difference  is  considered  to  be  the  residual 
valence. 


Residual  Valence  of  Various  Molecules  487 

The  computation  of  the  total  number  of  valences  in  a 
molecule  from  the  cohesion  is  made  from  van  der  Waals' 
factor  "a"  by  the  formula  :a  =  C(Mol.  Wt.  X  Val.  number) 2/3. 
a  was  computed  by  the  formula  already  given,  namely 
a  =  ((S2  —  S  +  2)/(S—  2))PcVc,in  which  S  is  the  critical 
coefficient  and  P6  and  Vc  the  critical  pressure  and  volume. 
The  constant  C  for  a  single  pair  of  molecules  was  assumed  to 
be  equal  to  (m2k)~/3,  in  which  m  is  the  gravitational  mass  of  a 
molecule  of  unity  molecular  weight  and  k  the  gravitational 
constant.  From  Millikan's  recent  determination  of  the  number, 
N,  of  molecules  in  a  gram  mol,  the  value  of  this  constant  was 
3.2015  X  io"37  expressed  in  dynes.  For  a  gram  mol  C  is 
1.177  X  ion. 

Owing  to  various  uncertainties  and  assumptions  in  the 
calculations,  this  method  of  determination  can  be  regarded 
only  as  of  the  nature  of  an  approximation  to  the  actual  amount 
of  residual  valence  of  molecules. 


Reprinted  fiom  THE  JOURNAL  OF  BIOLOGICAL  CHEMISTRY,  VOL.  XIV,  No.  5,  1913, 


AN  IMPORTANT  CHEMICAL  DIFFERENCE  BETWEEN 

THE  EGGS  OF  THE  SEA  URCHIN  AND 

THOSE  OF  THE  STAR-FISH. 

BY  A.  P.  MATHEWS. 

(From  the  Marine  Biological  Laboratory.  Woods  Hole.) 

(Received  for  publication,  April  21,  1913.) 

The  eggs  of  the  sea  urchin,  Arbacia  punctulata,  differ  markedly 
in  their  physiological  properties  from  those  of  the  star-fish,  Asterias 
forbesii.  The  sea-urchin  egg  is  remarkably  stable,  resistant  to 
oxidation,  has  a  very  low  rate  of  respiration  and  is  not  easily 
stimulated  to  artificial  parthenogenesis;  the  star-fish  egg,  on  the 
other  hand,  is,  after  maturation,  very  easily  oxidized,  has  a  rapid 
rate  of  respiration,  forms  sulphuretted  hydrogen  when  mixed  with 
sulphur,  is  easily  destroyed  by  oxygen,  easily  liquefied  by  heat 
and  is  easily  cytolyzed  by  anesthetics.  It  is  readily,  even  by  shock, 
caused  to  develop  parthenogenetically.  Moreover  after  matura- 
tion a  steady  growth  of  the  nucleus  takes  place,  whereas  in  Arbacia 
the  nucleus  after  maturation  remains  of  a  very  small  size. 

Five  or  six  years  ago  I  found  an  important  chemical  difference 
between  these  eggs  to  be  that  cholesterol  was  lacking  in  the  star- 
fish egg,  but  present  in  some  quantity  in  that  of  the  sea  urchin. 
In  view  of  the  relation  of  cholesterol  to  hemolysis  this  observation 
offers  a  possible  explanation  of  the  great  ease  of  cytolysis  of  the 
star-fish  egg  as  compared  with  the  sea-urchin. 

The  eggs  "were  pressed  from  the  ovary  through  cheese-cloth  to 
remove  the  connective  tissue,  and  the  mass  then  extracted  three 
times  with  a  large  amount  of  95  per  cent  alcohol,  boiling  for  one 
hour  each  time,  and  then  once  with  boiling  ether.  The  united 
extracts  were  evaporated  on  the  water  bath,  the  residue  extracted 
with  ether  repeatedly,  filtered  from  insoluble  substances,  and  the 
ether  poured  into  acetone.  The  fat  and  cholesterol  remain  in 
solution;  the  lecithin  is  precipitated.  The  acetone  filtrate  was 
evaporated  to  dryness,  the  oily  residue  saponified  with  alcoholic 

465 

THE  JOURNAL  OF  BIOLOGICAL  CHEMISTRY,   VOL.  XIV.  NO.  5. 


466      Chemical  Difference  in  Echinoderm  Eggs 

sodium  hydrate  and,  after  the  addition  of  sodium  sulphate  and 
some  water,  was  shaken  out  with  ether  repeatedly.  The  ether 
was  washed  several  times  with  sodium  carbonate  solution  and 
evaporated  to  dryness.  The  residue  was  very  small  in  amount, 
not  crystalline;  it  looked  like  oleic  acid.  It  gave  no  positive  tests 
for  cholesterol  either  by  Salkowski's  or  the  Liebermann-Burchard 
method.  I  have  repeatedly  sought  for  cholesterol  in  these  eggs 
varying  the  procedure  but  I  have  never  been  able  to  find  it.  On 
one  occasion  when  the  ovaries  were  not  ripe  the  fatty  residue  of 
the  ether  after  repeated  saponifications,-  both  with  alkali  and  acid, 
gave  a  very  faint,  transitory  green  such  as  cholesterol  gives  in 
the  Liebermann  test,  and  there  may  have  been  a  very  small  amount 
of  cholesterol  present,  but  no  crystals  could  be  obtained.  In  view 
of  the  fact  that  the  color  reaction  is  probably  not  specific  I  am 
doubtful  whether  there  was  a  trace  of  cholesterol  present  or  not. 
It  could  not  be  positively  identified.  It  may  be  mentioned  that 
cholesterol  in  combination  as  in  lanolin  gives  the  Liebermann-Bur- 
chard reaction  very  strongly. 

The  same  methods  applied  to  the  sea-urchin  egg  gave,  as  usual, 
a  crystalline  mass  on  evaporating  the  ether  after  saponification; 
the  crystals  looked  like  cholesterol  and  gave  a  typical  reaction 
of  Salkowski.  I  may  say  that  the  extract  of  the  whole  body  of 
the  star-fish  contains  cholesterol  in  abundance. 

Another  very  interesting  peculiarity  of  the  star-fish  egg  is  the 
character  of  its  phosphatide.  It  resembles  the  jecorin  described  by 
Drechsel.  A  large  quantity  of  eggs  was  extracted  with  hot  alcohol 
and  ether;  the  lecithin  (?)  precipitated  from  the  ether  solution  in 
the  usual  way,  redissolved  in  ether  (not  anhydrous)  and  reprecipi- 
tated  with  acetone  and  the  process  repeated  until  it  dissolved 
quite  clear  in  the  ether  and  did  not  settle  out  a  white  substance 
when  standing  in  the  cold.  This  white  substance  coming  out  of 
the  ether  had  a  sweet  taste,  but  had  no  reducing  action  on  Feh- 
ling's  solution  either  before  or  after  heating  with  hydrochloric  acid. 
The  phosphatide  thus  prepared  is  more  hygroscopic  than  lecithin 
from  the  brain  or  eggs.  It  makes  unusually  beautiful,  regular 
mye.in  forms  when  shaken  with  water,  and  it  seems  to  be  toxic 
for  sea-urchin  eggs.  It  was  probably  not  a  pure  substance.  It 
contains  a  large  amount  of  a  reducing  sugar  which,  calculated  as 
glucose,  amounts  to  10.51  per  cent  by  weight.  The  nature  of  this 


A.   P.  Mathews  467 

sugar  was  not  determined;  an  osazone  was  prepared;  the  fermen- 
tation test  was  indecisive.  The  lecithin  itself  does  not  reduce 
Fehling's  solution  but  only  after  it  has  been  heated  with  acid. 
I  heated  it  for  ten  hours  with  3.5  per  cent  HC1  and  determined 
the  sugar  by  the  reduction  of  Fehling's  solution  according  to  the 
method  of  Munson  and  Walker.  This  phosphatide  also  contains 
sulphuric  acid  in  an  ester  form  like  Koch's  sulphatide.  It  con- 
tained in  a  single  analysis  1.19  per  cent  of  sulphur  in  an  oxidized 
form.  This  is  in  organic  combination.  The  fatty  acids  are  very 
largely  oleic,  or  a  similar  acid,  having  an  ether-soluble  lead  salt, 
The  analysis  of  this  impure  phosphatide  resulted  as  follows: 

Glucose  (?) 10.51  per  cent. 

Fatty  acids 46.16  per  cent. 

Phosphorus 3.57  per  cent. 

Sulphur 1.19  per  cent. 

Of  the  fatty  acid  approximately  71.35  per  cent  was  recovered 
as  oleic  (?)  acid.  This  phosphatide  also  contains  a  considerable 
amount  of  magnesium,  but  I  did  not  determine  it  quantitatively. 

I  may  mention  that,  of  the  total  ether-soluble  portion  of  the 
alcohol-ether  extract  of  these  eggs,  the  lecithin  in  one  case  weighed 
0.6105  gram;  the  fat,  the  part  not  precipitated  by  acetone,  0.6055 
gram;  so  that  there  are  about  equal  quantities  of  fat  and  lecithin. 

SUMMARY. 

Cholesterol  is  either  absent  altogether  or  present  in  very  small 
amount  in  the  star-fish  egg.  It  could  not  be  positively  found  in 
the  eggs  of  Asterias  forbesii.  It  is  present  in  considerable  quan- 
tities in  the  sea-urchin  egg.  This  difference  possibly  is  correlated 
with  the  greater  sensitiveness  to  cytolysis  of  the  star-fish  egg.  The 
phosphatide  of  the  star-fish  contains  about  10  per  cent  of  a  re- 
ducing sugar  in  firm  combination  and  also  sulphuric  acid. 


Reprinted  from  the  American  Journal  of  Physiology 
Vol.  XXXII  — June  2,  1913  — No.  II 


CARBON  DIOXIDE  PRODUCTION  FROM  NERVE  FIBRES 
WHEN  RESTING  AND  WHEN  STIMULATED;  A 
CONTRIBUTION  TO  THE  CHEMICAL  BASIS  OF 
IRRITABILITY.1 

BY  SHIRO  TASHIRO 

[From  the  Department  of  Biochemistry  and  Pharmacology,  the  University  of  Chicago,  and  the 
Marine  Biological  Laboratory,  Woods  Hole,  Mass.] 

INTRODUCTION 

THERE  have  been  two  theories  of  the  nature  of  conduction  — 
one  upheld  among  others  by  Hermann,  that  it  was  a  prop- 
agated chemical  change;   the  other,  at  present  the  dominant  view, 
that  it  is  a  propagated  physical  change. 

In  1901  Professor  Mathews  suggested  2  that  it  was  in  the  nature 
of  a  coagulative  wave  propagated  along  the  fibre;  this  coagulation  of 
the  nerve  colloids  leading  either  directly  or  indirectly  to  the  electrical 
disturbance  accompanying  the  impulse.  At  the  time,  there  was  no 
evidence  of  chemical  change  in  the  nerve  fibre,  and  its  indefatiga- 
bility  seemed  to  point  to  an  absence  of  metabolism.  Certain  facts 
were  known,  however,  which  were  difficult  to  reconcile  with  this  phys- 
ical theory.  Darwin  had  observed  that  in  Drosera,3  conduction 
occurred  only  if  the  protoplasm  had  oxygen;  and  Mathews  4  observed 
that  salts  would  not  stimulate  a  nerve,  or,  at  any  rate,  their  power  of 
stimulation  was  much  reduced  if  the  nerve  remained  in  the  body  for 
a  time  after  death,  or  if  the  nerve  were  brought  into  the  salt  solution 
in  an  atmosphere  of  hydrogen.  This  clearly  indicated  a  dependence 
of^the  irritability  on  oxygen. 

1  The  preliminary  report  of  these  investigations  was  given  in  part  in  Bio- 
chemical section  of  Eighth  International  Congress  for  applied  chemistry,  Sep- 
tember, 1912.     See  original  communications,  Eighth  International  Congress  of 
applied  chemistry,  xxvi,  p.  163.     See  also  this  Journal  1913,  xxxi,  p.  xxii. 

2  Mathews:  Century  Magazine,  1902,  pp.  783-792;  Science,  1902,  xl,  p.  492. 

3  Insectivorous  Plants,  p.  57. 

4  Unpublished  observations. 


io8  Shiro  Tashiro 

This  fact  lead  to  a  search  for  evidence  of  the  chemical  nature  of 
irritability  and  in  a  number  of  papers  5  it  was  clearly  pointed  out  that 
the  anaesthetics  were  probably  acting  directly  in  a  chemical  manner 
instead  of  indirectly,  by  affecting  permeability,  and  that  probably 
the  anaesthetics  acted  by  uniting  with  the  protoplasm  where  02  usually 
took  hold.  This  view  was  strengthened  by  the  temperature  coeffi- 
cient of  conduction,  which  is  nearly  that  of  a  chemical  reaction;  by 
the  importance  of  C>2  for  artificial  parthenogenesis;  and  by  many  other 
facts  some  of  which  have  recently  been  collected  by  Haberlandt, 
Buijtendijk  and  others. 

Although  it  has  been  established  by  repeated  demonstrations,  that 
the  nerve  does  not  fatigue  under  ordinary  conditions,  as  measured 
by  the  method  used  in  muscular  studies,  yet  Frohlich  6  observed  that 
the  nerve  undergoes  certain  changes  by  long  activity.  Gotch  and 
Burch  discovered7  in  1889  that  if  two  stimuli  are  successively  set 
up  within  -%%-$  of  a  second,  only  one  negative  variation  is  produced. 
This  critical  interval,  or  refractory  period,  is  found  to  be  altered  by 
temperature  changes,  by  drugs,  asphyxiation,  and  anaesthetics.8 
Thus  by  prolonging  the  refractory  period  by  partial  anaesthesia,  Froh- 
lich easily  demonstrated  that  with  a  frequency  of  stimulation  less 
than  this  normal  refractory  period,  stimulation  of  the  attached  muscle 
no  longer  occurred.  He  interprets  this  as  a  phenomenon  of  fatiga- 
bility  of  the  nerve.  Thoner's  9  observation  seems  to  lead  to  a  similar 
interpretation,  for  he  found  recently  that  fatigability  is  less  effec- 
tive when  the  refractory  period  is  shortened  by  high  temperature. 
There  seems,  then,  to  be  fatigue  in  the  nerve,  but  it  cannot  be 
measured  by  an  ordinary  scale. 

After  the  complete  failure  of  the  chemical  detection  of  CO2  and 

6  A.  P.  MATHEWS:  Biological  bulletin,  1904-5,  viii,  p.  333;  this  Journal, 
1904,  xl,  p.  455;  ibid.,  1905,  xiv,  p.  203;  Biological  Studies  by  the  pupils  of 
William  Sedgwick,  1906,  p.  81;  Journal  of  pharmacology  and  experimental 
therapeutics,  1911,  ii,  p.  234. 

6  FROHLICH:  Zeitschrift  fur  allgemeine  Physiologic,  1903-4,  iii,  p.  445.    Ibid., 

P-  75- 

7  GOTCH  and  BURCH:  Journal  of  physiology,  1899,  xxiv,  p.  410. 

8  See  TAIT  and  GUNN,  Quarterly  journal  of  experimental  physiology,  1908, 
i,  p.  191;  TAIT,  ibid.,  1909,  ii,  p.  157. 

9  THONER:    Zeitschrift  fur  allgemeine  Physiologic,  1908,  viii,  p.  530;    ibid*, 
1912,  xiii,  pp.  247,  267,  530. 


Carbon  Dioxide  From  Nerve  Fibres  109 

acids  in  the  excited  nerve,  Waller  still  believes  that  it  must  give  off 
CO2  when  stimulated.  In  1896,  he  showed,  with  an  electro-physio- 
logical method,  that  among  other  reagents,  CO2,  in  minute  quanti- 
ties, increased  the  excitability  of  the  isolated  nerve  of  the  frog,  and 
that  the  normal  nerve,  when  excited,  also  increased  its  activity.10 
From  this  he  ingeniously  formed  the  hypothesis  that  every  activity 
in  the  nerve  fibre  must  be  associated  with  C02  production. 

That  there  may  be  CO2  production  in  the  nerve,  but  too  small  to 
be  measured  by  ordinary  methods,  is  shown  by  the  following  calcu- 
lations: A  frog  (Rana  temporaria)  gives  off  0.355  gram  of  CO2 
per  kilogram  per  hour  at  19  —  20°  C.11  A  small  piece  of  the  nerve 
fibre  of  the  same  animal,  say  i  cm.  in  length,  will  weigh  in  the  neigh- 
borhood of  10  milligrams.  Now,  if  the  mass  of  the  nerve  respires  at  the 
rate  of  the  whole  animal,  it  would  give  off  about  0.0000007  grams  of 
CO2  during  ten  minutes.  This  calculation  at  once  suggested  that 
the  lack  of  positive  evidence  of  metabolism  in  the  nerve  fibre  was 
not  at  all  conclusive  that  such  metabolism  did  not  occur,  in  view  of 
the  limitation  of  the  methods  for  the  estimation  of  C02.  It  was 
evidently  necessary  to  devise  methods  for  the  detection  of  very 
minute  quantities  of  CO2.  Thus  at  Professor  Ma  thews'  suggestion 
a  new  method  for  CO2  analysis  was  first  devised,  and  then,  under, 
his  direction,  I  have  undertaken  to  go  back  once  more  to  the  question 
of  CO2  production  in  the  nerve  fibre  during  the  passage  of  a  nerve 
impulse. 

To  study  the  nature  of  metabolism  involved  in  a  tissue,  one 
should  at  least  determine  the  oxygen  consumption  and  the  carbon 
dioxide  production.  Inasmuch,  as  the  present  problem,  however,  is 
concerned  only  with  direct  evidence  for  the  existence  of  metabolism 
in  the  nerve  fibre,  I  have  attempted  to  measure  C02  production 
only,  for  it  is  true  that  the  lack  of  oxygen  consumption  may  not 
necessarily  indicate  the  absence  of  chemical  changes,  while  the  pro- 
duction of  C02  will  surely  prove  the  presence  of  metabolism.  Further- 
more, as  CO2  production  is  the  only  sure  universal  expression  of  the 
respiratory  activity  in  anaerobic  and  aerobic  plant  and  animal  tissue 
in  normal  condition,  the  inquiry  of  CO2  production  in  an  excited  nerve 
will  not  only  concern  the  problem  of  the  nature  of  the  nerve  impulse 

10  WALLER:  Croonian  lecture,  Philosophical  transactions,  London,  1896. 

11  Taken  from  Pott's  figures.     See  figures  in  Table  ix,  p.  129. 


no  Shiro  Tashiro 

itself,  but  may,  also,  aid  in  forming  a  fundamental  conception  of  the 
tissue  respiratory  mechanism.  In  this  way,  if  the  protoplasmic  irri- 
tability has  a  direct  connection  with  the  cellular  respiration,  then 
our  idea  of  the  general  nature  of  the  pharmodynamics  of  many 
reagents  on  a  living  tissue  may  be  essentially  modified. 


METHODS  AND  MATERIALS 

Two  new  apparati  were  constructed  which  will  detect  CO2  in  as 
small  quantities  as  one  ten-millionth  of  a  gram  and  estimate  it  with 
quantitative  accuracy.  The  detailed  method  has  been  described  in 
a  separate  article.12 

Preliminary  experiments  with  these  new  apparati  showed  that  the 
sciatic  nerves  of  dogs  gave  too  large  quantities  of  CO2  for  my  method 
so  that  I  was  compelled  to  use  a  smaller  nerve  of  a  cold-blooded 
animal  for  quantitative  estimation.  For  exact  measurements  of  CO2 
production,  I  have  used  only  two  kinds  of  nerve,  although  I  have  used 
a  large  variety  of  nerves  in  qualitative  experiments.  For  a  non- 
medullated  nerve  fibre,  Prof.  G.  H.  Parker 1S  was  so  kind  as  to  sug- 
gest to  me  that  I  use  the  nerve  trunk  of  the  claws  of  the  spider  crab 
(Labinia  Caniliculata)  which  is  a  bundle  of  mixed  sensory  and  motor 
fibres.  The  frog,  whose  sciatic  was  used  as  a  representative  for 
medullated  nerve,  was  exclusively  Rana  pipiens,  obtained  from 
Indiana. 

As  my  apparati  in  the  present  form  cannot  be  used  for  a  muscle 
nerve  preparation  nor  for  the  normal  nerve  in  situ,  the  use  of  an 
isolated  nerve  could  not  be  avoided.  Experimental  factors  thus  intro- 
duced should  be  carefully  considered  before  we  interpret  the  observa- 
tion as  a  normal  metabolism.  This  serious  objection,  however,  can  be 
overlooked,  as  far  as  our  fundamental  question  of  different  metabolic 
activities  before  and  after  a  stimulation  is  concerned,  for  Waller  14 
has  demonstrated  that  the  presence  of  excitability  in  an  isolated 
nerve  persists  as  long  as  nineteen  hours  provided  that  the  electrical 
changes  correctly  represent  the  state  of  excitability.  Although 

12  See  pp.  137-145- 

13  For  this  and  other  suggestions,  I  am  under  great  obligation  to  Dr.  Parker. 

14  WALLER:   1896,  Brain,  xix,  p.  53. 


Carbon  Dioxide  From  Nerve  Fibres  in 

Herzen  claims  that  under  certain  conditions  of  local  narcosis  the 
nerve  fibre  may  give  an  action  current  without  any  muscular  con- 
traction (Wedenshi  and  Boruttau  both  deny  this),  and  Ellinson  15 
recently  demonstrated  by  the  use  of  cinchonamine  hydrochloride 
the  absence  of  negative  variations  without  abolishing  the  excitability 
of  the  nerve,  yet  evidences  are  now  abundant  to  indicate  that  the 
action  current  is  a  normal  physiological  phenomenon  in  uninjured 
tissue  expressing  the  simultaneous  activity  resulting  in  a  corre- 
sponding change  in  the  peripheral  organ.16  These  facts,  therefore, 
must  be  taken  as  showing  that  as  long  as  a  negative  variation  remains, 
the  nerve  is  probably  excitable;  and  that  the  phenomena  observed  in 
the  isolated  nerve  could  be  regarded  as  identical  with  that  of  a  nor- 
mal nerve  as  far  as  the  passage  of  a  nerve  impulse  in  an  isolated 
nerve  fibre  is  concerned. 


CO2  PRODUCTION  FROM  RESTING  NERVE 

In  this  study  of  the  metabolism  of  the  resting  nerve,  particular 
care  was  taken  to  select  those  fibres  which  were  free  from  nerve  cells. 
The  work  of  several  investigators 17  seems  to  indicate  that  tissue 
oxidation  is  primarily  concerned  with  the  cell  nucleus.  Inasmuch 
as  the  respiration  in  the  central  nervous  system  is  certain  18  and  the 
blood  supply  to  fibres  is  seemingly  scanty,  the  notion  persists  among 
certain  biologists  that  a  nerve  fibre  should  not  respire  since  it  has 
no  nucleus.  In  order  to  test  the  correctness  of  such  an  idea,  I  have 
studied  quantitatively  the  output  of  CO2  from  various  lengths  of  nerve 
which  are  known  to  be  free  from  nerve  cells.19  Here  is  the  result: 

15  ELLINSON:  Journal  of  physiology,  191 1,  xlii,  p.  i. 

16  For  further  details,  see:   GOTCH  and  HORSLEY:  Philosophical  transactions 
of  the  Royal  Society,  1891,  clxxii,  p.  514;  BERNSTEIN:   Archiv  fiir  die  gesammte 
Physiologic,  1898,  Ixxiii,  p.  376;   REID  and  MCDONALD:  Journal  of  physiology, 
1898-9,  xxiii,  p.  100;    LEWANDOWSKY:    Archiv  fiir  die  gesammte  Physiologic, 
1898,  Ixxiii,  p.  288;  ALCOCK  and  SEEMANN,  ibid.,  1905,  cviii,  p.  426. 

17  See  SPITZER:    Archiv  fiir  die  gesammte  Physiologic,  1897,  Ixvii,  p.  615; 
M.  NUSSBAUN:  Archiv  fur  mikroskopische  Anatomic,  1886,  xxvi,  p.  485;   R.  S. 
LILLIE:  This  Journal,  1902,  vii,  p.  412. 

18  L.  HILL:  Quoted  from  Hulliburton's  Chemistry  of  nerve  and  muscle,  p.  79. 

19  In  this  connection,  I  wish  to  express  my  indebtedness  to  Prof.  H.  H.  Donald- 
son for  his  kind  advice. 


ii2  Shiro  Tashiro 

Non-Medullated  Nerve  Fibre.  —  (The  nerve  of  the  spider  crab, 
and  apparatus  2  for  the  qualitative,  and  apparatus  i,  for  the  quanti- 
tative, estimations  were  used.)  When  I  place  the  nerve  of  a  spider 
crab  in  the  right  chamber  and  no  nerve  in  the  left,  and  watch  for  the 
deposit  of  barium  carbonate,  the  drop  on  the  right  will  soon  be  coated 
with  the  white  precipitate,  but  no  precipitate  whatever  is  visible  with 
a  lens  in  the  left.  ,C02  is  thus  shown  to  be  produced  by  this  resting 
nerve.  Now,  by  interchanging  the  nerve  from  the  right  to  the  left, 
no  nerve  being  in  the  right,  we  can  convince  ourselves  of  the  correct- 
ness of  this  conclusion,  by  eliminating  any  technical  error  which  might 
produce  the  different  results  in  different  chambers.  The  rate  at  which 
the  precipitate  appears  and  the  quantity  of  the  precipitate,  depends 
on  the  size  of  the  nerve.  In  fact,  C02  production  from  the  resting 
nerve  of  the  spider  crab  is  found  to  be  proportional  to  its  weight, 
other  things  being  equal,  and  is  constant:  For  10  milligrams  per  ten 
minutes  it  gives  6.7  X  -io-7  grams  at  15  —  i6°c. 

The  quantitative  determination  of  this  amount  is  made  in  the 
following  manner : 

The  claws  of  the  crab  are  carefully  removed,  and,  by  gently 
cracking  them,  the  long  fibre  of  the  nerve  trunk  is  easily  isolated. 
After  removing  the  last  drops  of  the  water  by  a  filter  paper,  the  nerve, 
with  the  aid  of  glass  chop  sticks,  is  carefully  placed  on  the  glass  plate,20 
and  quickly  weighed.  The  glass  plate  with  the  nerve  is  now  hung 
on  the  platinum  hooks  in  the  respiratory  chamber  A,  and  then  the 
.chamber  sealed  with  mercury.  The  analytic  chamber  is  now  filled 
with  mercury  in  the  manner  described  elsewhere,21  and  then  the 
apparatus  is  washed  by  C02  free  air  as  usual.  The  time  when  the 
barium  hydroxide  is  introduced  to  the  cup  in  chamber  B  is  recorded, 
and  the  stop-cock  between  the  two  chambers  is  closed.  When  at 
the  end  of  ten  minutes  the  drop  at  cut  F  is  perfectly  clear,  having  not 
a  single  granule  of  the  precipitate  visible  to  a  lens,  thus  insuring  that 
the  air  is  absolutely  free  from  CO2  then  a  known  portion  of  the  gas 
from  the  respiratory  chamber  is  introduced  into  the  chamber  below 
in  which  the  clear  drop  of  barium  hydroxide  has  been  exposed,  and  it 
is  determined  whether  or  not  the  amount  of  the  gas  taken  contains 

20  The  weight  of  this  plate  is  known  so  that  the  weight  of  the  nerve  can  be 
determined  very  quickly.     See  p.  120. 

21  See  pp.  139. 


Carbon  Dioxide  From  Nerve  Fibres  113 

enough  CO2  to  give  the  precipitate  in  ten  minutes.  If  it  does,  a  fresh 
nerve  is  prepared  and  a  less  volume  of  the  gas  is  withdrawn;  if  it 
does  not,  a  larger  volume  should  be  taken  till  the  precipitate  appears 
within  ten  minutes.  (See  footnote,  page  140.) 

In  this  way,  by  repeated  experiments  with  several  fresh  nerves, 
a  minimum  volume  of  the  gas  for  a  known  weight  of  the  nerve  which 
gives  a  precipitate  is  determined.  This  minimum  volume  should 
contain  exactly  a  definite  quantity  of  CO2  — namely  i.o  X  io~7 
gram.22 

In  this  way,  since  we  know  the  original  volume  of  the  respiratory 
chamber  from  which  this  minimum  volume  is  withdrawn,  and  since 
we  know  the  quantity  of  CO2  contained  in  this  volume,  it  is  easily 
calculated,  how  much  CO2  is  produced  by  the  nerve  during  the  known 
period.  It  should  be  understood  that  in  determining  the  minimum 
volume  of  gas  taken  from  the  respiratory  chamber,  a  series  of  experi- 
ments were  conducted  in  order  to  calculate  both  the  minimum  volume 
which  just  gives  the  precipitate  and  the  maximum  volume  which 
does  not  give  the  the  precipitate  for  a  known  weight  of  the  nerve  for 
a  known  period  of  respiration  In  the  tables  following,  columns  8 
and  9  refer  to  these  volumes  calculated  from  experiments. 

Table  I,  gives  the  result  for  a  non-medulla  ted  nerve. 

Medullated  Nerve  Fibre.  —  For  the  quantitative  estimation  of 
C02  production  from  the  medullated  nerve  I  have  taken  a  frog's 
sciatic,  using  apparatus  2.  The  results  given  in  Table  II,  obtained  by, 
similiar  methods,  show  that  each  ten  milligrams  of  the  frog's  sciatic 
nerve  gives  off  5.5  X  icr7  grams  for  the  first  ten  minutes. 

A  large  quantity  of  nerves  were  tested  and  it  was  determined 
whether  or  not  all  resting  nerves  give  off  CO2.  As  a  result,  I  found 
no  exception  in  any  of  them.  The  following  varieties  of  nerves 
were  examined: 

1.  MOTOR  NERVE:  Occulo-motor  nerve  of  the  skate.     (Raia  Ocallata.} 

2.  SENSORY  NERVE:  Olfactory  nerve  of  the  same.     (Raia  Ocallata.) 

3.  MEDULLATED  NERVE:    Sciatic  nerve  of  the  dog,  frog,  turtle,  mouse; 
•  optic  nerve  of  the  skate.     (Both  Raia  Ocallata  and  Raia  Erinecia.) 

4.  NON-MEDULLATED  NERVES:  Nerves  of  the  spider  crab;  olfactory  nerve 

of  the  skate.     (Raia  Ocallata.) 

5.  NERVE  OF  INVERTEBRATE:  Spider  crab's  nerves. 

22  See  p.  140. 


Shiro  Tashiro 


Carbon  Dioxide  From  Nerve  Fibres 


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JBy  glancing  at  the  columns  8  and  9  it  is  clear  that  2.70  c.c.  is  the  minimum  volume,  for  2.6  c.c.  is  maximum  volume  which  does  not 
give  the  precipitate.  Since  original  volume  of  respiratory  chamber  is  15  c.c.  we  have 
1.0  X  10-7  g.  X  £V  =  5-5  X  10-7  g.  C02  at  19°  -  20° 
2  Little  high  result  in  these  cases  is  no  doubt  due  to  high  temperature. 

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Shiro  Tashiro 


6.  NERVE  OF  VERTEBRATE  :  Nerves  of  frog,  dog,  mouse,  squiteague  (cynoscion 

Regalis),  and  skate.     (Both  Raid  Ocallata  and  Raia  Erinecia.) 

7.  NERVE  or  WARM-BLOODED  ANIMALS:  Those  of  dog,  mouse  and  rabbits. 

8.  NERVE  OF  COLD-BLOODED  ANIMALS:  Frog,  squiteague  (cynoscion  Regalis) 

and  skate.     (Both  Raia  Ocallata  and  Raia  Erinecia.) 

From  this  I  have  concluded  that  isolated  nerves  of  all  animals 
give  off  CO2.  It  remains,  now,  to  consider  whether  this  CO2  is  the 
product  of  normal  respiratory  activity  or  due  to  disintegration  of  the 
dead  tissue. 

IS   THE    C02    GIVEN   OFF   PRODUCED   BY  LIVING   PROCESSES? 

Comparison  of  Dead  and  Living  Nerves.  —  In  the  first  place,  it 
was  thought  that  if  C02  was  due  to  normal  metabolism  of  a  living 
nerve,  its  production  should  be  diminished  when  the  nerve  was  killed. 
The  following  result  (Table  III)  is  self  explanatory. 

TABLE  III 

COMPARISON  BETWEEN  NORMAL  AND  KILLED  (BY  STEAM)  NERVES  OF  SPIDER  CRAB 
123  4567 


Date 

Tempera- 
ture of 
room 

Weight  of 
nerve  in  mg. 

Stimula- 
tion 

c.c.  of  gas 
taken  from 
respiratory 
chamber 

Duration 
of 
respiration  : 
minutes 

Ppt.  of 
Ba(CO3) 
after  ten 
minutes 

Nov.  4 

13° 

40  (kiUed) 

no 

.5 

10 

- 

it         (C 

40  (killed) 

st'n 

.5 

10 

- 

"     5 

16  (normal) 

no 

1. 

10 

+ 

"     6 

15 

16  (killed) 

no 

1. 

12 

- 

"     7 

16 

16  (normal) 

no 

1. 

10 

+ 

Comparison  of  Anaesthetized  and  Non-Anaesthetized  Nerves.  — 
It  is  naturally  feared,  however,  that  the  killing  experiment  itself  may 
not  prove  that  C02  production  is  necessarily  due  to  the  living  mechan- 
ism, for  high  temperature  may  drive  off  C02  produced  already  by  the 
process  of  tissue  disintegration,  just  as  the  C02  diffused  out  from  a 
wet  thread  saturated  with  the  gas,  the  rate  of  diffusion  being  a  func- 
tion of  temperature.  Thus  anaesthesia  was  tried,  although  we  should 


Carbon  Dioxide  From  Nerve  Fibres 


117 


expect  at  the  outset  that  if  ether  had  no  direct  affect  on  the  respira- 
tory process,  as  some  physiologists  believe,  then  the  negative  results 
would  not  at  all  interfere  with  my  contention.  The  fact  is,  however, 
that  either  an  isolated  nerve  directly  treated  with  ether  vapor  or 
urathane,  or  the  nerve  isolated  from  a  deeply  anaesthetized  frog  gave 
a  much  less  quantity  of  CO%  than  the  normal  nerve  isolated  from  a 
normal  frog  whose  heart  has  been  cut  away  for  a  period  of  time  equal 
to  that  of  etherization.  Anaesthetics,  then,  diminish  CO2  production 
from  an  isolated  nerve  fibre.  These  experiments  are  being  continued 
quantitatively. 

CO 2  Production  of  Isolated  Nerve  at  Successive  Time  Intervals. 
—  It  was  also  thought  that  if  CO2  production  was  due  to  bacterial 
decomposition,  although  it  is  highly  improbable  for  such  a  fresh 
tissue,  we  may  expect  that  either  killing  by  steam  or  treating  with 

TABLE  IV 

SHOWING  DECREASED  CO2  PRODUCTION  BY  LONG-STANDING  (FROG'S  SCIATIC) 
123  4 


Temperature 
of  room 

Time  elapsed 
after  isolation 

Minimum  c.c. 
necessary  to  give 
J,  calculated  for 
10  mgs.  10  minutes 

Total  CO2  pro- 
duced from  nerve 
of  10  mg.  for  10 
minutes 

24° 

immediately 

2.7  c.c. 

5.5  X  10-7g.  CO2 

25 

1  hour 

7.08  c.c. 

2.1  X  10-7g.  COa 

24 

2  hours 

10.8  c.c. 

1.4  X  10-7g.  CO2 

24 

5.5  hours 

12.8  c.c. 

1.1  X  10-7g.  C02 

23.5 

7     hours 

15.3  c.c. 

.9  X  l(Hg.  C02 

23.5 

10.5  hours 

21.0  c.c. 

.6  X  10-7g.  C02 

24 

26     hours 

9.    cc.1 

1.6XlO-7g.C02 

24 

27.4  hours 

1.8.  c.c 

8.1  X  10-7g.  C02 

1  The  gradual  increase  at  this  point  should  be  noted  (after  26  hours,  it  is  clear  that 
bacterial  decomposition  sets  in). 

ether  would  check  the  C02  production,  and  that  the  results  observed 
above  may  not  necessarily  prove  that  C02  production  from  the  isolated 
nerve  fibre  is  due  to  a  respiratory  process.  Hence  a  number  of  the 
nerves  were  isolated  from  several  frogs  of  the  same  size  and  sex,  and 


n8  Shiro  Tashiro 

were  left  in  Ringer's  solution,  and  then  the  rate  of  the  gas  production 
is  determined  with  the  different  nerves  removed  at  successive  inter- 
vals of  time  from  the  Ringer's  solution  for  twenty-five  hours.  The 
interesting  results  given  in  Table  IV  not  only  show  that  CO 2  from  the 
fresh  nerve  is  not  due  to  bacterial  decomposition,  but  it  also  indicates 
that  when  such  abnormal  decomposition  sets  in,  the  output  of  gas 
takes  a  sudden  jump.  This  Table  further  shows  that  the  vital  process 
by  which  CC>2  is  produced  gradually  slows  up  as  the  tissue  approaches 
death,  indicating  that  the  decrease  of  CO2  production  is  parallel  to 
the  decrease  of  irritability  of  the  nerve. 

Increase  of  CO2  on  Stimulation.  —  The  most  convincing  evi- 
dence of  all  that  CC>2  is  formed  by  a  vital  process  is  the  fact  that 
a  stimulated  nerve  gives  off  more  CO2  (Part  II)  indicating  the 
presence  of  normal  metabolism  in  the  living  nerve  which  is  accelerated 
when  the  nerve  is  stimulated.  Thus  we  may  safely  conclude  here 
that  like  any  other  tissue  or  organs,  the  nerve,  too,  respires  whether 
it  has  a  nucleus  or  not,  and  that  the  rate  of  C02  production  is  pro- 
portionate to  its  weight,  other  things  being  equal. 


CO2  PRODUCTION  FROM  STIMULATED  NERVE 

We  have  now  come  to  our  main  inquiry,  namely,  is  there  any 
chemical  basis  for  irritability?  Just  what  relation  exists  between 
nervous  activity  and  chemical  changes  is  the  question  that  a  biologist 
should  consider  before  he  attempts  to  build  any  conception  of  the 
real  dynamics  of  living  matter.  For  it  is  the  phenomena  of  excita- 
bility in  the  nerve  fibre  that  has  stood  so  long  in  the  path  of  under- 
standing protoplasmic  irritability  in  general.  As  for  the  brain,  it  is 
now  established  that  certain  chemical  changes  are  involved  during 
stimulation  and  that  definite  chemical  changes  are  associated  with 
pathological  cases  either  in  its  chemical  composition  23  or  in  the  for- 
mation of  abnormal  metabolites.24  Aside  from  the  confused  facts 
concerning  histological  changes  in  the  ganglion  cells  of  fatigued  ani- 
mals, Hill  has  observed,  using  Ehrlich's  method  of  methylene  blue 

23  KOCH  and  MANN:  Archiv  of  neurology  and  psychiatry,  1909,  iv,  p.  44. 

24  DIXSON:  Journal  of  physiology,  1899-1900,  xxv,  p.  63;  CROFTAN:  American 
journal  of  the  medical  sciences,  1902,  p.  150. 


Carbon  Dioxide  From  Nerve  Fibres  119 

for  the  determination  of  the  rate  of  oxidation,  that  a  spot  of  cerebral 
surface,  if  stimulated,  loses  its  blue  color  owing  to  the  using  up  of  the 
oxygen.25  In  case  of  the  nerve  fibre,  however,  we  have  already  seen 
that  no  direct  evidence  has  ever  been  presented  to  show  any  chemical 
changes  connected  with  its  activity,  although  there  has  been  some 
indirect  evidence.  As  considered  before,  the  failure  of  the  direct 
detection  of  CO 2  from  the  stimulated  nerve  must  be  due  to  the  lack 
of  a  delicate  method.  Thus  using  the  new  method  we  have  already 
demonstrated  that  a  resting  nerve  gives  off  C02,  and  will  now  attempt 
to  prove  that  nerves  give  off  more  C02  when  stimulated.26 

Electrical  Stimulation  of  non-Medullated  Nerve.  —  Owing  to  the 
scope  of  delicacy  of  the  new  method,  which  is  sensitive  to  as  small  a 
quantity  as  i.o  X  io~7  gram  (an  amount  corresponding  to  the  CO2 
contained  in  -^  cc.  of  pure  air),  the  utmost  caution  must  be  taken  to 
prevent  any  complication  which  may  result  in  formation  or  absorption 
of  minute  quantities  of  C02.  After  I  had  found  by  experiment  that 
there  is  no  appreciable  increase  of  CO2  due  to  the  direct  electrical 
decomposition  in  the  nerve  when  stimulated  by  a  weak  induction 
current  and  that  several  other  forms  of  stimulation  qualitatively 
confirmed  the  results  obtained  by  the  electrical  stimulation,  I  have 
naturally  employed  the  induction  current  as  a  stimulant  in  all  my 
experiments  on  the  quantitative  estimation  of  CO2  production  from 
the  stimulated  nerve.27 

As  Table  V  shows,  the  stimulated  non-medullated  nerve  fibre  of 
the  spider  crab  gives  off  16.  X  io~7  grams  of  CO2  for  10  milligrams  of 

25  HILL:  loc.  cit. 

26  Professor  Carlson  has  very  kindly  called  my  attention  to  a  recent  publica- 
tion from  the  Physiologisch  Laboratorium  der  Utrechtsche  Hoogeschool,  in  which 
Buijtendijk  reports  that  certain  head  nerves  of  fishes  take  up  more  O2  when 
electrically  stimulated.     He  could  not,  however,  find  any  increase  of  O2  con- 
sumption  in   the   sciatic   of   the   frog.    Also  see:   Koninklijk  Akademie  van 
Wetenschappen,  Amsterdam,  afd,  xix,  pp.  615-621. 

Haberlandt  also  recently  reports  (Archiv  fur  Physiologic,  1911,  p.  419)  that 
the  resting  nerve  takes  up  of  O2,  41.7  -  33-4  cmm.  at  19°  -  24°  per  gram  per 
hour.  When  this  nerve  is  excited,  intake  of  O2  is  increased.  Since  the  respira- 
tory quotient  of  the  stimulated  nerve  is  equal  to  that  of  the  resting,  he  con- 
cludes that  when  the  nerve  is  excited,  it  must  give  off  more  CO2.  He  does 
not,  however,  indicate  how  much  CO2  is  produced  by  stimulation. 

27  Use  of  non-polarizable  electrodes  was  impossible  for  my  apparatus,  for  the 
presence  of  foreign  liquid  in  the  chamber  interferes  with  C02  estimation.     As 


i2o  Shiro  Tashiro 

nerve  for  ten  minutes,  while  a  fresh  resting  nerve  gave  only  6.7  by 
iQ-7  grams  for  the  same  units.  The  details  of  the  methods  are  as 
follows: 

The  nerve  of  the  claw  of  the  spider  crab  is  isolated  as  before.  A 
comparative  estimation  was  made  first.  Two  pieces  of  the  nerve  of 
equal .  weights  and  length  were  placed  separately  on  the  two  glass 
plates,  each  nerve  being  laid  across  the  electrodes  of  the  plate,  in  the 
manner  shown  in  Figure  i .  In  this  way  either  nerve  can  be  stimulated 
at  will.  These  glass  plates  are  hung  by  their  wires  upon  the  platinum 
wires  fused  into  the  side  of  the  apparatus,  these  wires  being  con- 
nected in  turn  with  the  induction  coil.  Under  this  condition,  when 
both  nerves  are  not  stimulated,  the  amounts  of  the  precipitate  are 
equal  in  both  chambers.  However,  when  one  of  the  nerves  is  elec- 

0 


FIGURE.  1.  Glass  weighing  plate.  A.  B.  Platinum  wire  fused  in  the  rear  of 
the  glass  plate,  with  hooks.  C.  The  nerve  which  is  stimulated  at  D. 
G.  The  plate  proper. 

I  have  the  other  piece  of  the  same  glass  out  of  which  this  plate  is  made.  This 
piece  of  glass  is  weighed  exactly  equal  to  this  weighing  plate,  so  that  any 
wet  tissue  can  be  weighed  very  quickly.  In  order  to  make  results  more  accu- 
rate, no  attempt  was  made  to  weigh  closer  than  |  milligram. 

trically  stimulated  (the  distance  between  the  primary  and  secondary 
coils  was  always  more  than  10  cm.  using  a  red  dry  battery,  the  current 
being  barely  perceptible  on  the  tongue),  not  only  does  the  precipitate 
appear  sooner  in  the  chamber  in  which  the  excited  nerve  is  placed, 
but  also  the  quantity  of  the  carbonate  is  much  greater. 

To  test  whether  the  increase  of  CO2  production  from  the  stimu- 
lated nerve  is  due  to  the  direct  decomposing  influence  of  the  current, 
or  to  the  increase  of  metabolism  produced  by  the  passage  of  a  nerve 

long  as  we  are  not  concerned  with  the  electrical  changes  in  the  nerve,  the  use  of 
platinum  electrodes  instead,  is  not  a  great  objection,  provided  that  the  current 
is  weak  enough  not  to  decompose  the  tissue  directly,  and  that  the  duration  of 
stimulation  is  not  very  long. 


Carbon  Dioxide  From  Nerve  Fibres  121 

impulse,  the  following  experiments  were  performed.  If  we  assume 
that  the  condition  under  which  an  electrical  decomposition  takes 
place  is  the  same -both  in  the  living  and  the  dead  nerve,  then  if  the 
increased  C02  is  due  to  the  current  itself,  we  should  expect  that  when 
a  killed  nerve  is  stimulated  by  a  current,  it  ought  to  increase  C02 
production  just  as  much.  When  I  placed  two  nerves  killed  by  steam 
in  each  chamber,  and  stimulated  only  one  of  them,  the  stimulated 
nerve  did  not  give  any  more  CO2  than  the  unstimulated,  using  the 
same  strength  of  current  employed  in  the  other  experiments.  In 
the  next  place,  it  was  thought  that  if  the  increase  of  CO2  is  due  to 
direct  electrical  decomposition,  not  limited  to  the  point  of  contact 
with  the  electrodes,  we  ought  to  get  a  proportional  increase  of  C02 
by  altering  the  distances  through  which  the  current  directly  passes. 
The  fact  was,  however,  that  we  could  produce  an  increase  of  C02 
production  by  stimulating  with  electrodes  2  mm.  apart  as  well  as  by 
15  mm.  apart.  Increase  of  C02,  therefore,  is  due  to  nervous  excita- 
tion and  not  to  the  direct  influence  of  the  electric  current  itself. 

With  this  consideration,  I  have  proceeded  to  make  a  quantitative 
estimation  of  CO2  from  the  stimulated  nerve  in  the  manner  described 
before.  The  results  are  shown  in  Table  V. 

Electrical  Stimulation  of  Medullated  Nerve.  —  With  apparatus 
2,  the  output  of  C02  from  the  excited  sciatic  nerve  of  the  frog  has  been 
quantitatively  estimated.  As  shown  below,  10  mgs.  of  the  sciatic 
nerve  gives  off  14.2  X  icr7  grams  of  CO2  during  ten  minutes  stimula- 
tion while  the  resting  nerve  of  the  same  animal  gave  off  5.5  X  io~7 
grams  for  the  same  units. 

Mechanical  Stimulation.  —  We  have  now  established  the  fact  that 
when  a  nerve  is  stimulated  by  an  electrical  stimulus,  it  gives  off  more 
C02.  In  order  to  prove  more  conclusively  that  this  CO2  production 
is  due  to  the  passage  of  a  nerve  impulse,  I  have  employed  several 
other  means  which  are  known  to  have  definite  influence  on  excita- 
bility of  the  nerve.  So  far,  the  use  of  these  methods  has  been 
confined  to  qualitative  experiments,  but  the  results  are  a  sufficient 
confirmation  of  the  observations  made  by  electrical  stimulation.  I 
cite  them  here  as  a  preliminary  report. 

Since  the  ordinary  method  for  mechanical  stimulation  cannot  be 
applied  directly  to  the  nerve  in  my  apparatus  in  its  present  form,  I 
used  a  different  method,  namely,  crushing  the  nerve.  That,  when  a 


122 


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124  Shiro  Tashiro 

protoplasm  is  smashed,  there  occurs  vigorous  chemical  changes,  is 
shown  by  several  investigators.  Fletcher 28  reports  that  injured 
muscle  gives  off  more  C02  than  the  normal. 

Later  he  and  Hopkins  29  discovered  that  muscle,  under  a  similar 
condition,  is  richer  in  lactic  acid. 

Dr.  Mathews  has  observed  a  similar  activity  in  crushed  eggs  of 
Arbacia.  Quite  accidently,  I  have  discovered  that  a  fresh  nerve,  too, 
when  crushed  with  the  rough  edge  of  a  glass  rod  gives  off  more  C02. 
This  increase  of  gas  production  from  the  injured  nerve,  I  take  to  be 
due  to  mechanical  stimulation.  To  test  this  hypothesis,  I  rendered 
the  nerve  unexcitable  by  means  of  ether  and  0.2  m.  solution  of  KC1, 
which  is  known  to  abolish  excitability  of  a  nerve.30 

Under  these  conditions,  I  observed  no  increase  of  gas  production 
when  the  nerve  is  crushed.  Therefore,  the  metabolism  existing  in 
the  living  nerve  must  be  accelerated  by  this  stimulation  when  it  is 
injured. 

This  interpretation,  however,  is  not  accordant  with  that  of  Fletcher 
and  Hopkins,  on  muscle.  In  studies  of  lactic  acid  formation  in  muscle, 
they  found  that  lactic  acid  is  spontaneously  developed,  under  anae- 
robic condition,  in  excised  muscle,  and  that  fatigue  due  to  contractions 
of  excised  muscle  is  accompanied  by  an  increase  of  lactic  acid.  In 
an  atmosphere  of  02,  there  is  no  survival  development  of  lactic  acid 
for  long  periods  after  excision.  From  a  fatigued  muscle,  placed  in 
62,  there  is  a  disappearance  of  lactic  acid  already  formed.  But  this 
disappearance  of  lactic  acid,  due  to  oxygen,  does  not  occur,  or  is 
masked,  at  supraphysiological  temperature  (e.  g.,  at  30  ).  Now 
traumatic  injury  to  an  irritable  muscle  too  produces  a  rapid  develop- 
ment of  acid.  Since,  however,  in  this  case  the  disappearance  of  lactic 
acid  due  to  O2  does  not  occur,  they  conclude  that  one  essential  condi- 
tion for  this  effect  of  oxygen  appears  to  be  the  maintenance  of  the 
normal  architecture  of  the  muscle.  Thus  they  contend  that  the 
increase  of  the  lactic  acid  by  mechanical  injury  is  not  due  to  stimula- 
tion, but  must  be  due  to  tissue  destruction. 

They,  however,  did  not  determine,  as 'far  as  I  know,  how  much 
the  output  of  CO2  is  affected  by  treating  the  injured  tissue  with  O2. 

28  FLETCHER:  Journal  of  physiology,  1898-9,  xxiii,  p.  37. 

29  FLETCHER  and  HOPKINS:  ibid.,  1906-7,  xxxv,  pp.  261,  288. 

30  MATHEWS:  This  Journal,  1904,  xi,  p.  463. 


Carbon  Dioxide  From  Nerve  Fibres  125 

Unless  it  is  proven  that  CO2  production  from  the  injured  muscle  is 
quantitatively  equivalent  to  lactic  acid  formed,  their  interpretation 
cannot  be  applied  to  the  injured  nerve,  for  in  the  case  of  the  "  plateau  " 
of  the  survival  muscle  respiration,  when  in  complete  loss  of  irritability, 
the  lactic  acid  yield  remains  stationary,  Hill  calculated  that  the  C02 
production  corresponds  to  the  amount  liberated  from  the  carbonate 
of  the  tissue  by  the  lactic  acid  formed.31 

Furthermore,  if  their  interpretation  is  applied  to  the  nerve,  the 
fact  that  etherized  nerves  or  nerves  rendered  unexcitable  by  KC1  do 
not  increase  CO2  output  when  crushed,  cannot  be  explained.  The 
fact  that  only  excitable  nerves  when  injured  increase  their  CO2  pro- 
duction, is  a  sufficient  proof  that  some  sort  of  stimulation  is  applied 
to  the  nerve  when  crushed,  the  tissue  destruction,  no  doubt,  following 
afterward.  The  increase  of  CO2  production  on  crushing  the  living 
nerve  and  its  absence  on  crushing  the  anaesthesized  nerve  is  the  point 
that  I  want  to  emphasize  here  in  order  to  confirm  my  results  obtained 
by  electrical  stimulation.  I  may  add  here  that  a  perfectly  parallel 
increase  of  CO2  by  crushing  has  been  observed  hi  dry  seeds,  including 
wheat,  wild  oats,  Lincoln  oats,  Swedish  select  oats,  leaves  of  Japanese 
ivy,  and  spinal  cords  of  rabbit.32 

Chemical  Stimulation.  —  The  study  of  the  nature  of  chemical 
stimulation  has  been  so  thoroughly  made 33  that  at  first  it  was  thought 
that  chemical  reagents  would  be  ideal  as  stimuli. 

It  was  soon  discovered,  however,  that  the  presence  of  minute 
quantities  of  a  foreign  liquid  is  such  a  disturbing  factor  that  stimula- 
tion by  salt  solutions  could  not  be  used  for  quantitative  experiments. 
With  a  qualitative  analysis,  however,  I  found  a  variety  of  evidences 
which  show  that  the  nerve* stimulated  chemically  gives  off  more  CO2, 
and  that  the  nerve  rendered  less  excitable  by  reagents  decreases  CO2 
production. 

When  each  sciatic  nerve  of  a  frog  is  isolated  and  one  is  left  in  the 
normal  saline  in  one  case,  and  in  the  body  of  the  frog  in  the  other,  for 
the  same  length  of  time,  and  then  transferred  to  the  two  chambers  of 
the  apparatus,  if  the  quantities  of  the  precipitate  are  compared,  it  is 
found  that  the  nerve  which  has  been  in  normal  saline  gives  more  CO2. 

31  HILL:  Journal  of  physiology,  1912,  xliv,  p.  481. 

32  Fuller  discussion  of  these  will  appear  in  a  subsequent  paper. 

33  MATHEWS:  This  Journal,  1904,  xl,  p.  4555  ^os,  riv»  P-  203- 


126  Shiro  Tashiro 

It  is  known  that  normal  saline  stimulates  frog's  sciatic  nerves.  The 
different  rates  at  which  CO2  is  produced  from  the  different  nerves 
treated  by  various  concentrations  of  KC1  is  equally  instructive.  It 
is  known  that  when  a  nerve  is  placed  in  a  molecular  solution  of  KC1, 
a  stimulation  takes  place  for  a  considerable  time.  Then  it  finally 
becomes  unexci table,34  whereas,  .2  m.  KC1  solution  abolishes  nervous 
excitability  in  a  short  time  without  primary  stimulation.  The  CO2 
production  follows  exactly  analogous  to  this.  The  nerve  treated  with 
the  stronger  solution  gives  more  CO2  than  that  of  a  weaker  solution. 
This  was  true  even  after  both  nerves  became  unexcitable,  showing 
that  the  nerve  must  be  giving  off  more  CO2  while  being  stimulated 
by  the  stronger  solution.  Although  my  quantitative  data  are  not 
complete  at  this  stage,  this  preliminary  statement  is  sufficient  to  show 
that  the  nerve  chemically  stimulated  gives  off  more  C02.  It  may 
be  added  in  passing  that  the  different  solubility  of  CO2  in  the  different 
concentrations  of  these  salts  solutions  cannot  explain  these  results 
solely  by  a  physical  interpretation,  for  there  is  not  enough  difference 
in  the  solubility  of  C02  in  dilute  equimolecular  solutions  of  KC1, 
and  NaCl,  whose  effect  on  C02  production  is  so  divergent,  the  former 
salt  diminishing,  the  latter  increasing  it. 

Heat  Stimulation.  —  It  may  be  recalled  in  Table  I  that  high  tem- 
perature increases  the  output  of  CO2  from  the  resting  nerve.  A 
respiratory  process  should  increase  proportionally  to  the  temperature. 
Raising  of  temperature,  however,  not  only  increases  the  rate  of  res- 
piration, but  also  (particularly  by  sudden  changes  of  it)  stimulates 
the  nerve.  A  very  interesting  fact  is  observed  in  connection  with 
the  killing  of  the  nerve.  When  the  nerve  is  killed  gradually  by  a 
slow  increase  of  temperature,  it  gives  off  more  CO2  than  when  killed 
suddenly,  the  determination  being  made  after  both  are  killed.  CO2 
production  from  the  dead  nerve  under  this  condition  must  be  due  to 
the  diffusion  of  the  gas  which  was  formed  previously,  just  as  Fletcher's 
dead  muscle  is  charged  with  C02  gas.  The  different  outputs  of  CO2 
between  slowly  killed  and  suddenly  killed  nerves  cannot  be  accounted 
for  unless  we  assume  that  in  one  case,  C02  is  produced  more  while 
being  killed  than  in  the  other.  Whether  such  increase  of  CO2  produc- 
tion, however,  was  due  to  the  acceleration  of  normal  respiration  by 
the  slowly  increasing  temperature,  or  due  to  direct  stimulation  caused 

34  MATHEWS:  loc.  cit. 


Carbon  Dioxide  From  Nerve  Fibres 


127 


by  heat,  or  due  to  both,  cannot  be  decided  here  unless  we  consider  the 
relation  between  excitation  and  tissue  respiration.35 

It  is  hoped  that  we  may  have  a  better  understanding  of  this  matter 
when  we  study  the  temperature  coefficient  of  normal  respiration  of  the 
nerve.  At  present,  we  are  satisfied  to  state  only  that  there  is  a  strong 
evidence  to  support  the  conclusion  that  heat,  ,too,  increases  C02 
production  from  the  nerve. 


DISCUSSION   OF   THE   RESULTS 

Comparison  of  Metabolism  of  Non-Medullated  and  Medullated 
Nerve.  —  Although  it  appears  ridiculous  to  attach  any  significance  to 
the  marked  similarity  in  the  magnitudes  of  C02  production  from  non- 
medullated  and  medullated  nerves,  the  temptation  is  irresistible  to 
comment  on  the  high  output  of  C02  from  the  non-medullated  nerve 
fibre.  Let  us  study  the  Table  following  (Table  VIII),  in  which  a 
summarized  comparison  is  given. 

TABLE   VIII 


Nerve 

CO2  from 
resting  nerve 

• 

CO2  from 
stimulated  nerve 

Rate  of 

increase 
of  CO2 

Non-medullated 
(spider  crab) 
Medullated  (frog) 

6.7  X  107  g.  (15°  -  16°  ) 
5.5  X  10-7  g.  (19°  -  20°  ) 

16.  X  107  g.  (14°    -  16°) 
14.2  X  107  g.  (20°  -  22°) 

2.4  times 
2.6     " 

Since  I  have  found  that  injury  increases  the  C02  production  from 
the  nerve,  the  values  I  have  obtained  from  cut,  or  isolated,  fresh 
resting  nerves,  such  as  I  had  to  use,  may  be  somewhat  greater  than 
the  output  of  normal  uninjured  nerves  would  be.  But  since  Alcock36 
has  shown  that  a  non-medullated  nerve  gives  a  higher  electrical 
response,  both  in  the  negative  variation  and  the  injury  current,  the 
C02  increase  due  to  the  cut  alone  will  probably  be  greater  in  case  of 
the  non-medullated  nerve  than  in  that  of  the  medullated  one.  That 
means  that  the  value  of  the  CO2  production  for  the  resting  uninjured, 

35  See  p.  134. 

36  ALCOCK:  Proceedings  of  the  Royal  Society,  1904,  Ixxiii,  p.  166. 


128  Shiro  Tashiro 

non-medullated  nerve  should  be  reduced  more  from  the  figures  found 
for.  the  isolated  nerve,  than  that  of  the  medullated  one.  In  other 
words,  by  lowering  6.7  X  io~7  gram  which  is  the  value  for  resting,  non- 
medullated,  isolated  nerves,  the  rate  of  increase  of  CO2  by  stimula- 
tion in  the  uninjured  nerve  would  become  higher  than  2.4  times,  and 
probably  higher  than  2.6  times,  which  is  the  rate  for  the  medullated 
nerve.  This  greater  effect  in  the  non-medullated  nerve  is  what  we 
should  expect  if  our  present  conception  that  conduction  is  in  the 
axis  cylinder  only,  is  correct.  Before  any  accurate  comparison  of 
the  increase  of  CO2  production  on  stimulation  of  non-medullated  and 
medullated  nerves  can  be  made  it  will  be  necessary,  however,  to 
determine  how  much  of  the  CO2  from  the  resting  nerve  is  due  to  injury 
alone.  Before  we  consider  this  point  seriously,  also,  we  should  deter- 
mine the  metabolic  activities  of  greater  numbers  of  nerves  of  different 
animals.  Such  an  investigation  is  at  present  useless  until  we  deter- 
mine more  quantitatively  the  relation  between  CO2  production  and 
the  various  strengths  of  stimulation  and  the  degree  of  excitability. 
'If  any  uniformity  of  C02  output  in  respect  to  anatomical  varia- 
tions is  discovered,  light  may  be  thrown  on  the  function  of  the 
medullary  sheath  and  other  differentiations. 

However  insignificant  these  results  may  be  as  far  as  the  similar 
rates  of  the  gas  production  of  these  two  nerves  is  concerned,  it  should 
be  strongly  emphasized  that  technical  error  plays  no  part  in  these 
determinations.  Inasmuch,  as  we  are  dealing  with  such  an  extremely 
small  amount  of  the  gas,  it  is  quite  natural  for  those  who  are  not 
familiar  with  my  apparati  to  suspect,  by  a  hasty  inspection  of  my 
results,  that  the  small  differences  I  found  under  different  metabolic 
conditions  may  be  due  to  mere  experimental  variations.  For  this 
reason,  particular  attention  is  called  to  a  detailed  description  of  the 
quantitative  method  I  used,  especially  the  footnote  on  page  144, 
where  I  have  cited  a  series  of  determinations  of  unknown  quantities 
of  CO2  in  testing  my  apparati.  I  may  repeat  here  that  my  experi- 
ments with  the  spider  crab  and  the  winter  skate  were  done  at  Woods 
Hole37  during  the  summer  of  1911,  while  those  with  the  frog  were 
done  in  Chicago  during  the  winter  of  1912.  Under  these  different 
conditions,  I  have  not  only  used  the  different  sizes  of  nerves,  but  also 

37  I  take  great  pleasure  in  acknowledging  my  indebtedness  for  the  kind  accom- 
modation offered  me  by  Drs.  Lillie  and  Drew  at  Woods  Hole. 


Carbon  Dioxide  From  Nerve  Fibres 


129 


experimented  with  two  different  apparati,  the  respiratory  chambers 
of  which  have  had  entirely  different  capacities.38 

Comparison  between  the  Metabolism  of  Resting  Nerves  and  that 
of  Other  Tissues.  —  To  compare  the  rate  of  metabolism  of  the  nerve 
with  that  of  other  tissues  is  a  matter  of  no  great  physiological  value 
on  account  of  great  variations  which  do  not  affect  equally  the  rate 
of  CO2  production.  Simply  to  give  a  better  picture  of  the  scope  of 
nervous  metabolism,  however,  let  us  make  the  following  comparison: 
Since  there  is  no  exact  determinations  made  on  either  the  other  organs, 
or  the  whole  animal,  in  the  case  of  the  spider  crab,  I  have  quoted  those 
of  the  nearest  Crustacea  of  which  data  are  available.  (Table  IX). 

TABLE  IX 


Animals 

C02  per  Kg. 
per  hour 

Temperature 

Determined  by  l 

Crustacea  (whole  animal) 

Jolyet  and  Regnaut 

Cray  fish  (Astacus)    . 
Crab  (Cancer  pagurus) 

37.7  c.c. 
89  9  c.c. 

12°.5 
16 

1C              ((                  " 

..obster  (Homarus  vulgaris)  .... 

54.4  c.c. 

15 

«    M     « 

^erve  of  spider  crab  (Labinia  cani- 
liculata) 

212  c.c. 

15°  -  16° 

Tashiro 

?rog: 
(Rana  esculenta)  (whole  animal)  . 

.082  gms. 

17 

Schultz 

(Rana  temporaria)  (whole  animal) 

.355    " 

19°  -  20° 

Pott 

(Rana  pipiens)  (sciatic  nerve)     . 

.33      " 

15 

Tashiro 

(Rana       temporaria  2)     (isolated 
muscle)        

.18      " 

21 

Fletcher 

Dog  . 

1.325    " 

Regnaut  and  Reiset 

.41      " 

Pettenkoffer  and  Voit 

.61      " 

«      « 

n      a     it 

.37      " 

Speck 

-  All  the  figures  are  quoted  from  Schafer's  Text  Book  of  Physiology  i,  pp.  702,  707  and 
708,  except  that  of  the  isolated  muscle  which  I  calculated  from  Fletcher  (toe.  a/.).  Fletcher 
fails  to  state  the  weight  of  a  leg,  but  gives  the  value  .2  c.c.  for  one-half  hour.  Hill  believes 
that  if  we  take  each  leg  6  g.  in  average,  the  value  will  not  be  far  from  the  truth. 

2  Fletcher  fails  to  state  the  species  of  the  frog,  but  it  is  inferred  from  Hill  s  paper. 

38  See  the  last  columns  of  Table  I  and  Table  II. 


130  Shiro  Tashiro 

Active  Nerves.  —  That  the  nerve  increases  its  CO2  production 
approximately  2.5  times  when  stimulated,  is  in  accordance  with  our 
conception  of  the  metabolism  of  other  acting  organs.  Just  how  much 
increase  of  CO2  takes  place  during  functional  activity  of  an  organ  or 
organisms  depends  on  conditions  as  well  as  on  habits  of  different  organs 
and  animals.  Pettenkofer  and  Voit 39  report  that  a  man  (weighing 
70  kgs.)  gives  off  when  working  0.76  grams  per  kg.  per  hour,  while 
resting  only  .56  gram.  Barcroft40  found  that  the  submaxillary  gland 
when  stimulated  by  the  chorda  tympani  gives  off  3-7  times  more 
CO2  than  the  resting  gland.  In  the  case  of  contracting  muscle,  the 
results  are  very  contradictory.  Hermann  41  found  that  the  contract- 
ing muscle  gave  off  9.3  per  cent  of  CO2  (by  volume)  while  the  resting 
one,  only  1.4  per  cent.  Tissot 42  and  other  workers  also  found  a 
similar  increase  of  CO2  from  contracting  muscle.  Minot,43  working 
with  Ludwig,  maintains  that  there  is  no  relation  whatever  between 
CO2  production  and  muscle  tetanus.  L.  Hill 44  and  Fletcher 45  both  con- 
firmed Minot's  work  by  finding  no  increase  of  CO2  production  from 
muscular  tetanus.  According  to  Fletcher,  the  increase  he  found  in 
C02  production  from  a  contracting  muscle  in  a  closed  vessel  is  due  to 
the  rigor.  Under  this  condition,  he  believes,  increased  formation  of 
lactic  acid  is  responsible  for  liberating  CO2  already  produced.  In 
either  case,  it  is  understood  that  functional -activity  in  the  muscle  is 
accompanied  by  an  increase  of  metabolic  activity.  It  is  difficult  to 
compare  this  increase  of  metabolic  activity  of  the  muscle  with  that 
of  the  nerve  unless  we  determine  how  much  and  what !  ind  of  metabol- 
ism takes  place  in  contracting  muscle. 

Respiration  Quotient  of  the  Nerve  Fibre.  —  As  quoted  before 
Haberlandt  found  that  a  resting  nerve  consumes  41.7  to  83.4  cmm. 
02  for  i  gm.  for  an  hour  at  19°  -  24°.  Although  he  has  not  deter- 
mined chemically  the  production  of  CO2  he  could  easily  read  the 
respiration  quotient  by  means  of  the  index  fluid.  Thus  he  found 

39  PETTENKOFER  and  VOIT:  loc.  cit. 

40  BARCROFT:  Ergebnisse  der  Physiologic,  1908,  vii,  p.  735. 

41  HERMANN:   Stoffwechsel  der  Muskeln,  Hirschwald,  Berlin,  1867. 

42  TISSOT:  Archives  de  physiologic,  1894-5,  (5)  vii.  p.  469. 

43  MINOT:  Arbeiten  aus  der  physiologischen  Anstalt  zu  Leipzig,  1868,  p.  i. 

44  L.  HILL:  See  Schafer's  Text  Book  of  Physiology,  1898,  i,  p.  911. 

45  FLETCHER:  Journal  of  physiology,  1898-9,  xxiii,  p.  68. 


Carbon  Dioxide  From  Nerve  Fibres  131 

that  the  respiratory  quotient  of  the  resting  and  acting  nerve  is  nearly 
unity.  Since  he  found  that  O2  consumption  is  increased  when  stimu- 
lated, and  since  the  respiration  quotient  remains  constant  before  and 
after  the  stimulation,  he  concluded  that  it  must  give  off  more  CO2 
when  stimulated.  It  is  very  interesting  to  compare  the  O2  consump- 
tion in  this  experment  with  the  CO2  production  of  mine.46 

Taking  his  lowest  figure,  because  he  worked  in  19°  -  24°  and  I  in 
19°  -  20°,  41.7  cmm.  of  O2  amount  to  .00007  cc-  f°r  jo  milligrams  for 
ten  minutes.  My  figure  of  5.5  X  io~7  grams  for  the  same  units  may  be 
translated  to  .00027  cc.  of  C02  (ignoring  temperature  and  pressure 

C02       00027 

correction).     Therefore-——  =  -       -  =  3. 8,  the  respiratory  quotient. 

O2         00007 

As  I  have  not  determined  O2  consumption  of  the  nerve  of  Rana  pipiens, 
this  figure  has  no  particular  value,  but  the  fact  that  the  CO2  produc- 
tion is  comparatively  higher  than  02  consumption  is  a  matter  of 
considerable  interest. 

One  of  the  most  important  observations  made  by  A.  V.  Hill 47 
is  the  fact  that  he  could  not  detect  any  rise  of  temperature  in  a  frog's 
nerve  as  measured  by  an  apparatus  which  is  sensitive  to  a  change  of 
one-millionth  of  a  degree.  From  this,  according  to  his  calculation, 
he  concludes  that  not  more  than  one  single  oxygen  molecule  in  every 
cube  of  nerve  of  dimension  of  3.7  //,  can  be  used  up  by  a  single  propa- 
gated nerve  impulse.  Therefore,  he  suggested  that  an  impulse  is 
not  of  irreversible  chemical  nature  but  a  purely  physical  change. 

Although,  I  confess,  my  ignorance  makes  it  impossible  to  interpret 
his  valuable  results  from  my  observations,  I  may  add  that  these  two 
apparently  irreconcilable  facts  may  throw  light  on  the  true  nature  of 
nervous  metabolism.  Dr.  Mathews  has  suggested  that  metabolism 
in  the  nerve  may  be  something  of  the  order  of  alcoholic  fermentation, 
which  is  not  a  direct  oxidation,  and  where  heat  production  cannot 
be  so  large  as  CO2  production,  since  the  energy  content  of  glucose  is 
only  a  trifle  higher  than  that  of  the  alcohol  produced.  The  compara- 
tively little  heat  production  in  the  case  of  working  glands  is  a  matter 
of  interest  in  this  connection.  At  any  rate  we  should  not  forget  the 

46  He  used  Rana  esculenta,  which,  by  the  way,  gives  for  the  whole  animal 
.082  g.  CO2  per  kg.  per  hour  at  17°  according  to  Schultz.  My  frog  was  Rana 
pipiens. 

47 'HILL:  Journal  of  physiology,  1912,  xliii,  p.  433- 


132  Shiro  Tashiro 

anatomical  as  well  as  the  chemical  differences  between  muscle  and 
nerve.  In  this  respect  the  ratio  between  CO2  production  and  02 
consumption  from  the  nerve  is  suggestive. 

The  extremely  small  intake  of  O2  has  another  point  of  interest  in 
relation  to  the  general  nature  of  irritability.  It  has  been  repeatedly 
reported  that  a  nerve  can  remain  excitable  several  hours  in  an  oxygen- 
free  atmosphere,  although  there  is  no  doubt  its  excitability  diminishes, 
yet  there  is  a  considerable  amount  of  evidence  to  show  that  oxygen 
is  very  closely  associated  with  the  state  of  excitability,  To  har- 
monize these  two  facts,  the  oxygen-storage  hypothesis  has  been 
suggested,  by  which  the  exhaustion  is  attributed  to  complete  consump- 
tion of  "the  stored  oxygen  and  that  excitability  is  restored  when 
atmospheric  oxygen  is  readmitted.  Without  committing  ourselves  to 
this  hypothesis,  I  may  add  that  according  to  Haberlandt's  figure,  the 
resting  nerve  of  10  milligrams  will  consume  only  .0042  cc.  O2  in  ten 
hours.  If  we  take  our  figure  and  assume  that  one  volume  of  oxygen 
was  necessary  to  produce  one  volume  of  C02  (this  assumption  is  made 
without  any  significance  except  to  give  a  liberal  estimate),  the  C02 
production  would  require  about  .015  cc.  of  O2  for  ten  hours.  And  if 
we  assume  again  that  activity  will  increase  O2  consumption  in  propor- 
tion of  C02  production,  then  it  means  that  the  nerve  when  stimulated 
takes  up  only  .03  cc.  of  O2  during  ten  hours  stimulation.  I  am  not 
aware,  at  present,  of  the  existence  of  any  method  which  will  surely 
remove  O2  as  completely  as  this  from  a  large  vessel;  and  this  is  a 
very  liberal  estimate.  My  experiences  in  rendering  the  air  free  from 
CO2  encourages  me  to  raise  the  question,  How  can  one  remove  every 
trace  of  02  from  a  nerve  fibre?  Without  having  a  correct  criterion 
for  an  oxygen-free  medium  we  cannot  at  present  consider  definitely 
any  question  of  the  relation  of  O2  to  irritability. 


CONCLUSION 

In  spite  of  all  the  negative  evidence  against  the  presence  of  meta- 
bolism in  the  nerve  fibre,  we  have  established  three  important  facts: 
namely,  (i)  A  resting  nerve  gives  off  a  definite  quantity  of  carbon 
dioxide;  (2)  stimulation  increases  CO2  production;  and  (3)  CO2 
production  from  the  resting  nerve  proportionally  decreases  as  irri- 


Carbon  Dioxide  From  Nerve  Fibres  133 

tability  diminishes.  These  facts  prove  directly  that  the  nerve  con- 
tinuously undergoes  chemical  changes,  and  that  nervous  excitability 
is  directly  connected  with  a  chemical  phenomenon.  There  is  still 
another  question  left,  namely,  Is  there  any  direct  relation  between 
excitability  and  tissue  respiration?  To  put  this  question  more  directly, 
we  may  ask:  Does  excitability  depend  on  the  respiratory  process  in 
the  protoplasm?  To  answer  these  questions  we  must  refer  to  two  facts; 
namely  the  direct  relat  on  between  the  rate  of  respiratory  activity  and 
the  decrease  of  excitability;  secondly,  the  influence  of  reagents  on 
CO 2  production  and  their  effects  on  the  state  of  excitability. 

By  the  studies  of  C02  production  by  Fletcher  48  lactic  acid  forma- 
tion by  Fletcher  and  Hopkins,49  and  heat  evolution  by  A.  V.  Hill,50 
it  has  been  established  that  in  isolated  muscle,  respiratory  processes 
decrease  when  irritability  diminishes.  In  the  case  of  the  nerve, 
as  shown  in  Table  3,  C02  production  reaches  this  minimum  when 
excitability  approaches  zero.  These  relations,  however,  do  not  show 
conclusively  that  the  protoplasmic  irritability  depends  on  respiratory 
activity,  for  it  is  quite  probable  that  the  dying  nerve  may  alter  its 
physical  condition  as  well,  which  according  to  the  physical  school, 
may  consequently  alter  the  state  of  excitability. 

That  irritability  is  independent  of  the  respiratory  processes  has 
been  hitherto  successfully  contended  in  the  case  of  the  dry  seed.  The 
works  of  Horace  Brown,  Thisel ton-Dyer  51  and  others  indicate  that 
the  dry  seed  can  be  kept  alive  at  the  conditions  where  no  ordinary 
gaseous  exchanges  are  possible.  It  is  argued,  therefore,  that  life  is 
possible  without  any  metabolic  activity.52  While  a  definite  poten- 
tiality for  irritability  may  exist  without  any  metabolic  activity,  yet 
that  the  irritability  can  persist  without  respiratory  activity,  or  vice 
versa,  is  a  matter  by  no  means  settled.  In  the  case  of  ordinary 
air-dry  seed,  Waller  could  demonstrate  the  response  of  electrical 
changes  when  stimulated  although  the  detection  of  CO2  was  impossi- 

48  FLETCHER:  loc.  cit. 

49  FLETCHER  and  HOPKINS:  loc.  cit. 

50  A.  V.  HILL:  loc.  cit. 

51  THISELTON-DYER:    Proceedings  of  the  Royal  Society,  1897,  Ixii,  p.  160; 

ibid.,  Ixv,  p.  361. 

52  I  am  indebted  to  Professor  Crocker  for  his  kind  suggestion  as  to  botanical 

literature. 


134  Shiro  Tashiro 

sible.  This  failure,  however,  as  he  himself  expected,  was  due  to  the 
lack  of  delicacy  of  the  chemical  methods  for  detecting  C02.  I  ob- 
served, with  my  apparatus  that  even  a  single  kernel  of  a  dry  seed 
gives  off  a  definite  quantity  of  CO2  as  long  as  it  is  alive.  In  ordinary 
condition  not  only  a  living  dry  seed  gives  off  more  CO2  than  the  dead 
one,  but  also  like  the  nerve,  it  always  gives  off  more  CO2  when  stimu- 
lated by  mechanical  injury.  In  the  normal  condition,  therefore,  we 
may  safely  conclude,  there  is  always  metabolic  activity  as  long  as 
the  seed  is  irritable,  and  that  in  the  different  states  of  irritability, 
the  respiratory  activity  is  proportionately  different.  At  present, 
therefore,  we  have  no  decided  evidence  which  will  prevent  us  from 
considering  excitability  as  a  function  of  respiration  under  ordinary 
conditions.  This  relation  is  more  directly  studied  by  the  use  of 
anaesthetics. 

I  have  already  demonstrated  that  an  etherized  nerve  gives  off 
considerably  less  CO2  than  the  normal.  Such  an  etherized  nerve  will 
not  give  more  CO2  when  it  is  crushed.  This  may  be  interpreted 
by  some  to  mean  that  the  etherized  nerve  may  be  already  dead. 
This,  however,  is  not  the  case.  This  objection,  also,  I  have  considered 
by  studying  the  nerve  treated  with  KC1. 

When  the  nerve  is  treated  with  .2  m  KC1  and  then  crushed,  it  does 
not  give  an  increase  of  CO2  production.  Mathews  has  shown  that 
while  a  .2  m.  KC1  solution  renders  the  nerve  unexcitable,  yet  it  will 
recover  its  excitability  by  being  replaced  into  n/8NaCl.  These  two 
facts,  therefore,  support  the  idea  that  any  agents  that  suppress  excita- 
bility of  the  nerves  also  decrease  the  C02  production  and  that  C02 
production  by  crushing  the  nerve  must  be  largely  due  to  stimulation. 
This  hypothesis  is  strikingly  supported  by  similar  observations  on 
the  dry  seed.  Etherized  seeds  give  much  less  CO2  and  cannot  be 
stimulated  to  give  more  C02  by  crushing,  while  under  normal  con- 
ditions, crushing  a  seed  always  increases  its  CO2  production.  Quan- 
titative experiments  in  this  direction  will  be  given  in  another  paper. 

These  facts  directly  support  Mathews'  hypothesis  that  substances 
which  suppress  irritability  must  act  on  the  tissue  respiration  pri- 
marily. If  such  an  hypothesis  is  correct,  we  can  easily  picture  what  is 
happening  in  the  nerve  fibre.  Vernon 53  considers  that  a  tissue 
contains  certain  substances  which  can  absorb  oxygen  from  their  sur- 

53  VERNON:  Journal  of  physiology,  1909-10,  xxxix,  p.  182. 


Carbon  Dioxide  From  Nerve  Fibres  135 

roundings  to  form  an  organic  peroxide,  and  by  the  help  of  a  peroxidase 
can  transer  this  to  amino  acid  and  carbohydrate  molecules  bound  up 
in  the  tissue,  just  as  H2  O254  can  oxidize,  with  the  help  of  an  activator, 
an  acid  of  formula  R.  CHNH2  COOH  to  C02,  NH3  and  an  aldehyde 
RCHO,  and  then  oxidize  this  aldehyde  to  RCOOH  and  ultimately  to 
CO2  and  H2  O.  Poisons  such  as  HNC,  NaHS03  and  NaF,  which  he 
found  to  decrease  CO2  production,  temporarily  paralyzed  respiration, 
he  thought,  by  uniting  with  aldehyde  groups,  while  formaldehyde,  acid 
and  alkali  temporarily  paralyze  C02  forming  power  of  the  tissue  by 
destroying  the  peroxidase.  The  organic  peroxide,  though  it  can  still 
affect  some  oxidation,  cannot  of  itself  carry  it  to  the  final  C02  stage. 
Recovery  of  CO2  forming  power  is  due  to  the  regeneration  of  the 
peroxidase. 

Although  I  doubt  that  such  a  process  occurs  in  nervous  respiration, 
the  idea  of  two  similar  metabolic  phenomena  involved  in  the  nervous 
metabolism  is  very  helpful  to  understand  the  behavior  of  the  nerve 
during  continued  activity.  Most  recently  Tait  discovered  that  a 
refractory  period  has  two  phases,  absolute  and  relative.55  When 
he  treated  the  sciatic  nerve  of  a  frog  with  yohimbine,  the  relative 
phase  is  greatly  prolonged,  while  the  absolute  one  is  little  affected, 
a  result  quite  different  from  other  common  anaesthetics.  Waller56 
has  already  observed  that  protoveratrin  slows  up  the  positive 
variation  of  the  nerve,  while  the  negative  variation  is  little  in- 
fluenced. Waller  contends  that  this  drug  does  not  alter  cata- 
bolic  change,  but  retards  anabolic  activity  to  a  considerable 
degree.  Since  pharmocological  action  on  animals  of  protoveratrin 
and  yohimbine  are  very  similar,  Tait  concludes  that  these  drugs 
must  attack  the  nerve  in  similar  manner,  and  that  a  refractory  period, 
too,  must  consist  of  two  phases  corresponding  to  the  catabolic  and 
anabolic  processes  which  Waller  observed  in  the  case  of  protovera- 
trinized  nerves.  Thus,  he  considers  that  his  "  absolute  phase"  of 
the  refractory  period  corresponds  to  negative  variation  or  catabolic 
process  of  the  nerve,  and  the  "  relative  "  to  the  positive  return  or 
anabolic.  Yohimbine,  in  other  words,  retards  anabolic  processes  con- 
siderably, thus  prolonging  the  refractory  period,  or  increasing  nerve 

64  DAKIN:  Journal  of  biological  chemistry,  1908,  iv,  pp.  63,  77,  8 1,  227. 
55  TAIT:  Journal  of  physiology,  1912,  xl,  p.  xxxviii. 
66  WALLER:  Brain,  1900,  xxiii,  p.  21. 


136  Shiro  Tashiro 

fatigue  easily.  These  considerations  suggest  very  strongly  that  the 
absence  of  fatigability  in  the  nerve  as  measured  by  the  ordinary 
methods,  is  not  a  question  of  absence  of  metabolism,  but  merely  the 
speed  by  which  these  two  processes  come  to  an  equilibrium. 

Although  we  have  an  infinite  number  of  facts  still  unexplainable, 
by  our  present  knowledge  of  nerve  physiology,  we  have  established  a 
few  new  facts  around  which  we  may  build  up  some  idea  concerning 
this  most  essential  phenomena  of  living  matter, — i.e.,  irritability. 
As  to  the  true  nature  of  the  nerve  impulse,  I  can  only  confess  my 
ignorance. 

SUMMARY 

1.  All  nerve  fibres  give  off  CO2.     The  resting,  isolated  nerve  of 
the  spider  crab  produces  6.7  X  icr7  gram  per  10  milligrams  per  ten 
minutes.     The  frog's  sciatic  5.5  X  io~7  grams. 

2.  When  nerves  are  stimulated  they  give  off  more  CO2.    .The 
nerve  of  the  spider  crab  claw  produces  16.  X  io~7  gram  when  stimu- 
lated, the  frog  nerve  14.2  X  icr7  grams.     The  rate  of  increase  of 
C02  by  stimulation  amounts  to  about  2.5  times. 

3.  The  CO2  output  of  resting  nerve  is  due  to  a  vital  active  process. 

4.  Anaesthetics  greatly  reduce  the  carbon  dioxide  output  of  nerves 
and  dry  seeds. 

5.  Mechanical,  thermal  and  chemical  stimulation  also  increases 
the  carbon  dioxide  output  of  nerves. 

6.  Single  dry  living  seeds  (oat,  wheat,  etc.)  react  in  most  par- 
ticulars similar   to   nerves  as   regards   their   irritability,   relation  to 
anaesthetics,  mechanical  stimulation  and  carbon  dioxide  outputs. 

7.  The  general  conclusion  is  drawn  that  irritability  is  directly 
dependent  upon  and  connected  with  tissue  respiration  and  is  primarily 
a  chemical  process.     These  results  strongly  support  the  conception 
that  conduction  is  of  the  nature  of  a  propagated  chemical  change. 

To  Prof.  A.  P.  Ma  thews,  under  whose  direction  I  have  carried  on 
these  experiments,  I  express  my  appreciation  and  gratitude.  For 
many  suggestions,  I  am  under  obligation  to  Dr.  F.  C.  Koch. 


Reprinted  from  the  American  Journal  of  Physiology 
Vol.  XXXII  — June  2,  1913  — No.  II 


A  NEW  METHOD  AND  APPARATUS  FOR  THE 

ESTIMATION  OF  EXCEEDINGLY  MINUTE 

QUANTITIES  OF  CARBON  DIOXIDE 1 

BY  SHIRO  TASHIRO 

[From  the  Department  of  Biochemistry  and  Pharmacology,  the  University  of  Chicago,  and  the 
Marine  Biological  Laboratory,  Woods  Hole,  Mass.] 

IN  connection  with  the  study  of  the  metabolism  of  the  nerve  fibre, 
I  undertook,  at  the  suggestion  of  Prof.  A.  P.  Mathews,  to  work 
out  a  method  for  the  detection  of  exceedingly  minute  quantities  of 
carbon  dioxide.  Following  a  suggestion  made  by  Dr.  H.  N.  McCoy, 
a  very  simple  method  was  devised,  which  I  reported  first  to  the 
Chicago  Section  of  the  American  Chemical  Society; 2  later  in  con- 
junction with  Dr.  McCoy,  its  further  details  were  reported  to  the 
Analytic  Section,3  of  the  Eighth  International  Congress  of  Applied 
Chemistry.  The  principle  of  the  new  method  is  as  follows : 

1.  Exceedingly  minute  quantities  of  carbon  dioxide  can  be  precipi- 
tated as  barium  carbonate  on  the  surface  of  a  small  drop  of  barium 
hydroxide  solution. 

2.  When  a  drop  of  barium  hydroxide  is  exposed  to  any  sample  of 
gas  free  from  carbon  dioxide,  it  remains  perfectly  clear,  but  when 
more  than  a  quite  definite  minimum  amount  of  carbon  dioxide  is  intro- 
duced, a  precipitate  of  carbonate  appears,  detectable  with  a  lens. 

3.  By  determining,  therefore,  the  minimum  volume  of  any  given 
sample  of  a  gas  necessary  to  give  the  first  visible  formation  of  the 
precipitate,  its  carbon  dioxide  content  can  be  estimated  accurately, 
since  this  volume  must  contain  just  the  known  detectable  amount  of 
carbon  dioxide. 

1  One  of  these  apparati  was  described  at   the  biochemical  section,  Eighth 
International  Congress  of  applied  chemistry,  September,  1912;  see  also,  Journal 
of  biochemistry,  1913,  xiv,  p.  xli. 

2  May  18,  1912. 

8  Original  Communication:  Eighth  International  Congress  of  applied  chemis- 
try, 1912,  i,  p.  361. 


138 


Shiro  Tashiro 


I  have  constructed  two  apparati,  based  on  this  principle,  which 
are  especially  adapted  for  the  estimation  of  the  output  of  carbon  diox- 
ide for  very  small  biological  specimens.  With  these  apparati,  one 
cannot  only  detect  easily  a  very  small  amount  of  gas,  given  off  by  a 
small  dry  seed,  or  a  small  piece  of  a  frog's  sciatic  nerve,  but  can  also 
estimate  it  with  considerable  accuracy. 

The  apparatus  shown  in  Fig.  i 
consists  of  two  glass  bulbs.  The 
upper  bulb  A,  is  a  respiratory 
chamber,  having  a  capacity  of  about 
15  c.c.,  which  can  be  diminished  to 
9  c.c.  by  means  of  mercury.  The 
lower  bulb  B  is  an  analytic  chamber 
with  a  volume  of  25  c.c.,  which  can 
be  made  to  5  c.c.  by  filling  up  with 
mercury.  These  two  bulbs  are  con- 
nected with  a  capillary  stop-cock  D. 
The  respiratory  chamber  is  fitted 
with  a  tight  glass  stopper,  R,  which 
is  connected  to  a  three-way  capillary 
stop-cock  C.  This  glass  stopper  is 
so  arranged  that  the  chamber  can 
be  sealed  by  putting  mercury  above 
the  stopper. 

The  tubes  are  thick  walled  capillaries  of  about  i  mm.  internal 
diameter,  excepting  upturned  tubes  inside  the  bulbs,  which  should 
be  rather  thin  walled,  especially  at  F  and  H,  where  it  is  widened  to  an 
internal  diameter  of  about  2  mm.  It  is  important  that  the  glass  of 
which  these  tubes  are  made  should  be  of  a  quality  not  readily  attacked 
by  barium  hydroxide. 

The  details  of  the  method  of  procedure  are  as  follows : 

The   apparatus   is   first   cleaned   and   dried.4    The   specimen   is 

4  The  apparatus  is  made  in  such  a  way  that  it  can  be  cleaned  and  dried  in 
ten  minutes  without  being  taken  apart.  For  this,  the  stop-cock  D  is  closed  and 
E  and  L  are  opened.  The  arm  at  L  is  connected  to  the  suction  pump.  Then 
a  little  acidulated  water  is  introduced  through  G.  By  closing  E,  and  opening  D 
and  G,  the  excess  of  water  is  drained  off.  Then  the  process  is  repeated  with  dis- 
tilled water,  alcohol,  and  alcohol  ether.  The  last  drying  is  completed  by  passing 
a  current  of  air  through  G  while  D  is  closed. 


FIGURE  1 
One-third  the  actual  size. 


Apparatus  For  Estimating  Carbon  Dioxide  139 

placed  on  a  glass  plate  5  and  weighed.  The  glass  plate  is  hung  on 
n  and  m,  which  are  electrodes  fused  into  the  side  of  the  respiratory 
chamber  A.  The  chamber  is  now  closed  with  the  stopper  R  and 
sealed  with  mercury.  Through  L,  a  connection  is  made  with  a 
pump  6  and  about  20  c.c.  of  mercury  is  introduced  through  G.  Not 
too  much  mercury  should  be  used;  its  surface  should  not  be  within 
5  mm.  of  the  cup  F.  Then  wash  the  whole  apparatus  with  carbon 
dioxide-free  air,7  which  is  introduced  through  C,  by  successive 
evacuations.  After  the  evacuation  and  washing  out  with  pure  air, 
which  is  repeated  three  or  four  times,  the  pressure  inside  of  the  bulbs 
is  made  equal  to  the  atmospheric  pressure  by  adjusting  it  at  the  nitro- 
meter in  the  usual  fashion.  Stop-cock  E  is  then  closed,  and  the 
space  between  E  and  L  is  evacuated  so  that  the  barium  hydroxide 
can  rush  in,  a  process  which  is  very  advantageous  to  obtain  a  clear 
barium  hydroxide  solution.  Then  clear  barium  hydroxide  solution 
is  run  in  through  L.  By  opening  E  very  slowly  and  carefully,  the  solu- 
tion is  now  introduced  into  the  chamber  so  that  a  small  drop  stands 
up  upon  the  upturned  end  of  the  capillary  at  F.  Then  the  connection 
between  the  two  chambers  is  closed  by  D.  It  is  imperative  that  this 
drop  of  the  solution  should  be  perfectly  clear  at  the  start.  If  no 
deposit  of  barium  carbonate  forms  on  the  surface  of  the  drop  within 
ten  minutes,8  a  portion  of  the  sample  gas  is  drawn  into  B  by  with- 
drawing mercury  through  G  and  opening  the  stop-cock  D.  The 
volume  of  mercury  withdrawn,  which  may  be  readily  determined  by 
volume,  or  more  accurately  by  weight,  gives  the  volume  of  the  sample 

5  The  kind  of  glass  plate  used  in  connection  with  the  nerve  and  small  animals 
like  Planaria  is  shown  on  p.  120,  Fig.  i.     (The  first  paper.) 

6  The  pump  should  be  capable  of  giving  a  vacuum  of  at  least  25  or  30  mm.  of 
mercury. 

7  Air  cannot  be  freed  completely  from  carbon  dioxide  by  passing  it  through 
wash  bottles.    In  my  work,  carbon  dioxide-free  air  is  prepared  by  shaking  air  with 
twenty  per  cent  solution  of  sodium  hydroxide  in  a  tightly-stoppered  carboy,  fitted 
with  suitable  tubes.     When  this  is  to  be  used,  it  is  driven  into  a  nitrometer  which 
is  filled  with  less  concentrated  alkaline  solution  (a  weak  solution  is  used  so  that 
the  chamber  may  not  be  too  dry)  by  displacing  it  by  running  in  a  solution  of 
sodium  hydroxide.    After  each  evacuation,  this  air  is  introduced  from  the  nitro- 
meter into  the  chamber  A  through  stop-cock  C. 

8  If  no  precipitate  appears  within  ten  minutes,  it  is  a  sure  control  that  the 
apparatus  is  free  from  carbon  dioxide. 


140  Shiro  Tashiro 

gas  taken  from  the  respiratory  chamber,  since  the  pressure  in  A  and 
B  is  kept  equal  to  the  atmospheric  during  the  transfer. 

One  now  watches  the  surface  of  the  drop  at  F  with  a  lens  to  see 
whether  any  formation  of  barium  carbonate  occurs  within  ten  minutes. 
With  this  apparatus,  I  have  repeatedly  introduced  accurately  known 
quantities  of  carbon  dioxide  of  very  high  dilution  into  B  in  the  manner 
just  described  and  as  a  result  have  found,  with  remarkable  regularity, 
that  i.o  X  io~7  gram  of  carbon  dioxide  is  the  minimum  amount 
which  will  cause  a  formation  of  barium  carbonate  within  a  period  of 
ten  minutes.  Smaller  amounts  of  carbon  dioxide  give  no  visible 
results;  while  larger  amounts  give  a  deposit  more  rapidly,  and  appear 
in  larger  quantities.  This  minimum  detectable  amount  'i.o  X  io~7 
gram  is  about  the  amount  which  is  contained  in  J  c.c.  of  natural  air, 
in  which  we  assume  3.0  parts  of  carbon  dioxide  in  10,000  by  volume.9 

In  order  to  determine  the  concentration  of  carbon  dioxide  in  the 
respiratory  chamber,  one  must  first  find,  for  the  apparatus  used,  the 
minimum  detectable  amount  of  carbon  dioxide.  Then  one  finds,  by 
trial,10  the  minimum  volume  of  gas  necessary  to  give  the  first  visible 
formation  of  barium  carbonate.  This  volume  must,  therefore,  con- 
tain the  known  minimum  detectable  amount  of  carbon  dioxide.  From 
the  ratio  between  this  volume  and  the  original  volume  of  the  respira- 
tory chamber,  out  of  which  this  amount  is  withdrawn,  the  absolute 

9  LETTS  and  BLAKE:  Proceedings  of  the  Royal  Dublin  Society,  1899-03,  ix, 
p.  107. 

10  In  the  case  of  biological  problems,  when  the  specimen  gives  off  carbon 
dioxide  continuously,  and  sometimes  at  different  rates,  varying  with  the  time,  it 
is  much  simpler  not  to  attempt  to  determine  the  minimum  volume  by  a  continuous 
trial  with  the  same  sample;  but  instead  to  repeat  the  experiments  with  a  series 
of  samples  of  known  weights  for  a  known  time,  and  determine  the  minimum 
volumes  which  give  the  precipitates,  and  the  maximum  volumes  which  do  not 
give  the  precipitates.     In  this  way,  it  can  easily  be  calculated  what  is  the  mini- 
mum volume  which  gives  the  precipitate  for  the  given  weight  of  the  specimen  for 
a  given  time.     Table  I  on  page  1 14  will  illustrate  this  more  clearly. 

Another  upturned  cup  H  provided  in  the  respiratory  chamber  A  is  used  in 
case  only  the  qualitative  detection  of  C02  is  wanted.  In  such  a  case,  the  perfectly 
clear  barium  hydroxide  solution  is  introduced,  after  the  necessary  cleaning  and 
washing,  to  the  respiratory  chamber,  forming  the  usual  drop  at  H  instead  of  F. 
It  should  be  noted  that  in  case  a  smaller  capacity  is  necessary  for  the  respiratory 
chamber,  the  mercury  is  introduced  by  a  pipette  to  the  bottom  of  the  chamber 
at  K. 


Apparatus  For  Estimating  Carbon  Dioxide 


141 


quantity    of    carbon    dioxide,    given    by    the   specimen,    may    be 
computed. 

At  the  suggestion  of  Dr.  F.  C.  Koch,  another  apparatus  was  con- 
structed, which  provides  a  control  drop  of  the  barium  hydroxide 
solution,  side  by  side  with  the  other.  The  apparatus  (Biometer)  shown 
in  Fig.  2,  although  it  appears  complex,  is  nothing  more  than  apparatus 
i,  inclined  90°,  but  each  of  its  chambers  is  provided  with  a  barium 
hydroxide  cup  d  and  f .  It  is  made  of  glass  consisting  of  two  respi- 
ratory chambers,  serving  also  as  analytic  chambers,  connected  by  a 
three-way  stop-cock  L,  the  other  arm  of  which  is  connected  to  one 
arm  of  another  three-way  stop-cock  K.  Each  of  the  other  two  arms 
of  stop-cock  K  is  connected  to  a  nitrometer  W  and  X.  The  nitro- 


FIGURE  2.     Biometer,  one-third  actual  size. 
The  shaded  portions  of  the  apparatus  indicate  the  rubber  connection  which  is  first 


coated  by  shellac,  and  then  sealed  with  a  special  sealing  wax. 
also  sealed  with  mercury. 


Some  parts  are 


meter  on  the  right,  is  connected  to  a  carboy  with  air  free  of  CO2;  and 
the  other,  on  the  left,  to  a  similar  reservoir  with  air  free  of  C02  plus 
any  gas  which  is  desired  as  a  medium  for  conducting  the  experi- 
ment. Chamber  A  is  drawn  to  a  capillary  stop-cock  C;  chamber  B 
is  drawn  to  the  three-way  stop-cock  G,  one  arm  of  which  is  con- 
nected with  a  mercury  burette  T,  which  is  used  for  adjusting  the 
pressure.  Both  of  the  chambers  have  a  capacity  of  20  to  25  c.c. 
and  are  provided  with  a  pair  of  platinum  electrodes  n  and  m,  and 
also  with  the  glass  stoppers  S  and  R,  which  can  be  sealed  as  usual 
with  mercury.  The  pump  is  connected  through  J,  and  the  barium 


142  Shiro  Tashiro 

hydroxide  solution  is  introduced  through  V  to  d  and  f,  where  drops 
are  formed  as  before. 

As  stated  above,  this  apparatus  can  be  used  for  the  combined 
purposes  of  qualitative  detection,  quantitative  estimation,  and  com- 
parative determination  of  the  output  of  C02  from  the  various  biolog- 
ical specimens.  It  has  a  decided  advantage  over  the  other  in  the 
fact  that  we  have  a  control  drop,  side  by  side,  under  exactly  the  same 
conditions,  and  that  the  comparative  estimation  of  C02  produced  by 
different  specimens  can  be  made  very  easily  and  accurately.  The  de- 
tailed method  of  procedure  is  described  under  three  different  headings : 

(a)  For  the   Qualitative  Detection  of  Carbon  Dioxide.  —  After 
the  apparatus  is  cleaned  and  dried,11  a  weighed  tissue  is  placed  on  the 
glass  plate  and  hung  on  n  and  m  of  the  chamber  A,  and  no  tissue  in 
the  other  chamber.     After  both  chambers  are  closed  with  the  stop- 
pers S  and  R  and  sealed  with  mercury,  they  are  so  filled  with  mercury 
that  the  remaining  volumes  in  both  chambers  are  now  exactly  the 
same.     The  chambers  are  now  evacuated  and  washed  with  pure  air. 
When  evacuation  and  washing  with  pure  air  is  complete,  the  pressure 
is  made  atmospheric,  by  adjusting  with  the  nitrometer  the  connec- 
tion between  A  and  B  is  then  closed  with  stopcock  L.     If  any  CC>2 
is  given  off  by  the  tissue,  the  desposit  of  carbonate  will  soon  appear 
on  d,  while  in  the  control  chamber  the  drop  on  f  remains  perfectly 
clear.     In  order  to  avoid  any  possible  error  of  a  technical  nature  this 
experiment  is    repeated   by   exchanging   the    chambers,    now   using 
chamber   B   for  the  respiratory  chamber    and    the   other   A   as   a 
control. 

(b)  For   Comparative   Estimation   of   CO2  from   Two   Different 
Samples.  —  By   repeated   quantitative    experiments,    it   was   found 
that  the  speed  with  which  the  first  precipitate  appears  and  the  sizes 
of  the  deposits  on  the  drops  at  d  and  f  represent  corresponding  quanti- 
ties of  carbon  dioxide.     Thus  with  remarkably  simple  means,  we  can 
determine  simultaneously  the  comparative  outputs  of  the  gas  from  two 
different  tissues  or  from  the  same  tissues  under  different  conditions. 
The  method  of  procedure  is  best  illustrated  by  the  following  example. 
Two  pieces  of  the  sciatic  nerve  are  isolated  from  the  same  frog  and 
exactly  weighed.     One  piece  is  laid  on  one  glass  plate,  and  the  other 

11  This,  too,  can  be  cleaned  and  dried  without  being  taken  apart.  See  foot- 
note on  p.  138. 


Apparatus  For  Estimating  Carbon  Dioxide  143 

on  the  other  plate  in  such  a  way  that  one  part  of  the  nerve  lies  across 
the  electrodes  of  the  glass  plates  as  shown  in  Fig.  i,  page  120.  In 
this  way,  when  the  plates  are  hung  on  the  electrodes  i>  and  m,  any 
desired  nerve  can  be  stimulated  with  the  induction  current.  These- 
plates  are  now  hung  on  the  electrodes  in  each  chamber,  and  the  usual 
procedure  is  followed  for  the  cleaning  and  the  washing  of  the  appara- 
tus to  make  it  CO2  free.  After  the  connection  between  the  two 
chambers  is  closed  by  means  of  stop-cock  L,  the  nerve  in  chamber 
A  is  stimulated  by  the  current.  Then  if  one  can  watch  over  the 
surfaces  of  the  drops  carefully  from  the  start,  he  finds  the  first  deposit 
of  the  carbonate  on  cup  d  of  chamber  A  in  which  the  stimulated  nerve 
is  placed.  Later,  the  total  amount  of  the  precipitates  grows  much 
larger  in  the  case  of  this  cup.  This  increased  output  of  the  carbon 
dioxide  from  the  stimulated  nerve,  thus  observed,  can  be  duplicated 
by  repeating  the  similar  experiment,  after  exchanging  the  chambers, 
as  usual.  This  comparative  estimation  can  be  more  accurately  made 
by  exact  quantitative  measurement,  the  method  for  which  the  follow- 
ing will  illustrate. 

(c)  For  Quantitative  Measurement  of  Gas.  —  The  detailed 
method  is  exactly  analogous  to  that  of  apparatus  i.  Here  we  use 
chamber  B  as  the  respiratory  chamber  and  A  as  the  analytic  cham- 
ber. Barium  hydroxide  should  be  introduced  into  chamber  A  only 
at  d,  and  the  stop-cock  F  is  always  closed  except  at  the  time  of  wash- 
ing. The  pressure  should  be  adjusted  by  mercury  burette  T,  or  by 
the  potash  bulb  of  the  nitrometer.  In  case  the  mercury  burette  is 
used,  the  remaining  volume  in  the  respiratory  chamber  should  be 
recorded.12  The  introduction  of  a  known  amount  of  gas  from  the 
respiratory  chamber  B  to  the  analytic  chamber  A  is  accomplished 
by  withdrawing  the  mercury  from  C  into  a  very  narrow  graduated 
cylinder,  while  the  stop-cocks  L  G  and  H  are  opened.  After  a  quick 
adjustment  of  the  mercury  burette  to  equalize  the  pressure,  the  stop- 
cock L  is  closed  and  the  presence  of  carbonate  is  looked  for  exactly 
in  the  same  manner  as  described  in  connection  with  the  other  appara- 
tus, determining  the  minimum  volume  that  gives  the  precipitate  for 
the  known  mass  of  tissue  for  a  known  time. 

12  The  bulbs  are  marked  at  the  point  where  their  capacity  became  15  c.  c. 
by  introducing  mercury.  The  variation  of  capacity  can  easily  be  read  by  noting 
the  mercury  burette. 


144  Shiro  Tashiro 

In  summarizing,  I  may  emphasize  the  following  points: 

1.  Particular  care  must  be  taken  to  test  the  air- tightness  of  the 
apparatus. 

2.  Purifying  the  air  must  be  done  with  greatest  care,  as  this  is 
essential. 

3.  The  apparatus  must  be  perfectly  dry. 

4.  A  weak  suction  pump  cannot  be  compensated  by  frequency  of 
washing. 

5.  As  long  as  the  ratio  between  the  c.c.  taken  from  the  chamber 
and  the  original   volume    of   the  chamber   is   needed,    it  is    most 
important  to  have  the  pressure  in  A  and  B  equal  to  the  atmos- 
pheric.    If  this  is  accomplished  we  can  neglect  any  caution  against 
pressure  and  temperature  variations  —  a  correction  which  is  always 
necessary  for  ordinary  methods  of  analysis  of  exceedingly  minute 
quantities  of  any  gas. 

In  devising  this  method  and  in  constructing  this  apparati,  I  am 
under  great  obligation  to  Professors  McCoy  and  A.  P.  Mathews  and 
to  Dr.  F.  C.  Koch. 

In  order  to  test  the  accuracy  with  which  an  estimate  of  concen- 
tration of  carbon  dioxide  could  be  made,  many  determinations  were 
carried  out  with  samples  of  air  which  contained  accurately  known 
concentrations  of  carbon  dioxide  prepared  by  Dr.  F.  C.  Koch.  The 
experimenter  did  not  learn  the  concentrations  of  the  samples  until 
after  the  analysis  had  been  completed.  In  making  up  the  test  sam- 
ples, pure  carbon  dioxide,  made  by  heating  sodium  bicarbonate  was 
diluted  with  the  carbon  dioxide  free  air  several  times  in  succession, 
as  illustrated  by  the  following  example:  5.5  c.c.  of  pure  carbon  diox- 
ide was  diluted  to  52.0  c.c.  over  mercury  and  thoroughly  mixed; 
5.5  c.c.  of  the  first  mixture  was  diluted  to  52.0  c.c.;  i.i  c.c.  of 
the  second  was  diluted  to  50.7  c.c.;  of  this  third  mixture  5.6  c.c. 
was  received  from  Dr.  Koch.  I  diluted  this  a  fourth  time  to 
255.6  c.c.  to  form  a  mixture  to  be  analyzed.  The  following  observa- 
tions were  made:  0.5  c.c.  was  introduced  into  the  apparatus  and  pro- 
duced no  precipitate  in  ten  minutes;  0.5  c.c.  more  of  the  same  sample, 
gave  no  precipitation  in  another  interval  of  ten  minutes;  0.5  c.c. more, 
a  total  of  1.5  c.c.,  was  run  into  the  bulb.  In  six  minutes  the  first 
evidence  of  a  precipitate  appeared  on  the  surface  of  the  drop  at 
d  of  apparatus  2  and  in  eight  minutes  was  well  developed.  Since 


Apparatus  For  Estimating  Carbon  Dioxide 


145 


the  amount  of  carbon  dioxide  required  to  give  the  precipitate  is  i.o 
X  io~7  grams,  this  amount  is  contained  in    1.5  c.c.  of  the  sample 
or    i    c.c.    contained   6.7  X  icr8  grams  of    carbon    dioxide.       The 
amount  of    carbon  dioxide   actually  contained  in  the  sample   was 
5-5  X  5-5  X  7-1  X  5-6 
52  X  52  X  50.7  X  255-6  C'C'  =  6"  X  I0 
In  six  such  determinations,  all  made  with  samples   the   concentra- 
tion of  which  were  unknown  to  the  experimenter  at  the  time  of  the 
analysis,  the  results  given  in  the  following  table  were  obtained: 


Volume  of  sample  re- 
quired to  give  a 
precipitate 

Weight  of  carbon  dioxide  in  one  c.c. 

Found 

Taken 

1.0    c.c. 

1.0    X  10-7  g. 

0.92  X  10-7  g. 

.5    c.c. 

2.      X  107  g. 

2.3    X  10-7  g. 

.55  c.c. 

1.82  X  10-7  g. 

1.83  X  10-7  g. 

1.5    c.c. 

.67  X  10-7  g. 

0.62  X  10-7  g. 

2.25  c.c. 

.45  X  10-7  g. 

0.45  X  10-7  g. 

ERRATA 

IN  JUNE  NUMBER  OF  THE  AMERICAN  JOURNAL  OF  PHYSIOLOGY 
(VOL.  XXXII,  No.  II) 

Substitute  " apparatus"  for  "apparati"  in  the  following  places: 

Page  no,  lines  7,  n,  23. 
Page  129,  line  i. 
Page  137,  line  28. 
Page  144,  line  16. 

Substitute  "7.1  cc."  for  "  i.i  cc."  on  page  144,  line  29. 

In  figure  i,  page  120,  correct  as  indicated  in  the  following  drawing 


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